the function f is defined by f(x)=e−x(x2 2x) . at what values of x does f have a relative maximum?

Answers

Answer 1

Answer:f

Step-by-step explanation:

its not that hard

Answer 2

The function is concave up for  x < 1 and concave down for x > 1 because the second derivative is positive for x < 1 and negative for x > 1. As a result, the critical point at x  < 1 is a relative maximum.

What is function?

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is common to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

The derivative of the function f(x) can be found by taking the derivative of the expression e^(-x) (x^2 + 2x) using the product rule:

f'(x) = -e^(-x) (x^2 + 2x) + e^(-x) (2x + 2) = 2e^(-x) - 2xe^(-x) (x + 1)

Setting f'(x) equal to zero and solving for x gives us the critical points:

0 = 2e^(-x) - 2xe^(-x).(x + 1)

2xe^(-x).(x + 1) = 2e^(-x)

x(x + 1) = e^x

x^2 + x - e^x = 0

Next, we determine the concavity of the function at the critical points by analyzing the second derivative of the function:

f''(x) = 2e^(-x) + 2xe^(-x) + 2xe^(-x).(x + 1) - 2e^(-x).(x + 1)

= 2e^(-x).(1 - x)

Since the second derivative is positive for x < 1 and negative for x > 1, the function is concave up for x < 1 and concave down for x > 1. Thus, the critical point at x < 1 corresponds to a relative maximum.

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Related Questions

Annabelle and Eric made 17ounce of pizza dough they ue 5/8 of the pizza dough to make pizza and ue the ret to make roll what i the difference between the amount of dough they ue to make pizza and the amount of dirty ue to make roll?

Answers

The difference between the amount of dough they use to make pizza and the amount of dirty use to make roll is 4.25 ounce. The result is obtained by using calculations in fractions.

How to count a set of objects using fractions?

Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.

For example:

1/4 (one-fourth)2/5 (two-fifth)

It means one of four parts and two of five parts.

Annabelle and Eric made 17 ounce of pizza dough.

5/8 of the pizza dough is used to make pizza.The rest is used to make roll.

Find the difference between the amount of dough they use to make pizza and the amount of dirty use to make roll!

To make pizza, the pizza dough they use is

= 5/8 × 17 ounce

= 85/8 ounce

= 10.625 ounce

To make roll, the pizza dough they use is

= 17 - 10.625 ounce

= 6.375 ounce

The difference amount of the usage is

= dough to make pizza - dough to make roll

= 10.625 ounce - 6.375 ounce

= 4.25 ounce

Hence, the difference amount of dough to make pizza and dough to make roll is 4.25 ounce.

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how to determine density of a liquid with cubes, a meterstick and stopwatch

Answers

The formula to determine the  density of a liquid with cubes, a meterstick and stopwatch is density of the liquid = mass / volume = 2.7 g / (volume of liquid displaced by the cube)

Density is a measure of how much mass is contained in a given volume of a material. In order to determine the density of a liquid, you will need three things: cubes, a meterstick, and a stopwatch.

First, gather your materials and select a cube of known dimensions. Place the cube on the surface of the liquid and start the stopwatch. Observe how long it takes for the cube to sink to the bottom of the container. Let's call this time t.

Next, use the meterstick to measure the height of the liquid in the container

With these two pieces of information, you can calculate the density of the liquid using the formula:

=> density = mass / volume

The mass of the cube can be calculated as:

=> mass = volume * density of the cube

where the volume of the cube is given by

=> volume = s³, where s is the length of one side.

Since we know the length of one side (s = 1 cm), the volume of the cube is 1 cm³.

The density of the cube can be assumed to be a constant value (for example, if the cube is made of aluminum, the density is approximately 2.7 g/cm³).

So,

=> mass = volume * density of the cube = 1 cm³ * 2.7 g/cm³ = 2.7 g.

The volume of the liquid displaced by the cube can be calculated as:

volume = mass / density of the liquid = mass / (h/t²)

where h/t² is the acceleration due to gravity.

Finally,

density of the liquid = mass / volume = 2.7 g / (volume of liquid displaced by the cube)

Complete Question:

Determine the density of an unknown liquid with only a meterstick, stopwatch, and cubes that sink.

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Which of the following T-tables would NOT be an appropriate model for the function shown here?

Answers

The second table has the points:

f(2) = 0

f(2) = 1

So it isn't even a function, that is the correct option.

Which of the given tables is not an appropiate model of the function?

Here we have the graph of function x = f(x), where the values of x are shown on the horizontal axis and the values of f(x) ares hown on the vertical axis.

Something that you can see, is that when x = 0 (leftmost value) we have:

f(0) = 2.

So every table should have that, but if we look tat the second option we can see that:

f(2) = 0

f(2) = 1

So that table has tw different values for x = 2 (so it does not even represent a function). So that is the correct option.

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Solving systems by elimination
4x - 6y = 16
-4x+8y=-8

Answers

2y=8
y=4

4x-24=16
4x=40
x=10

y=4, x=10

Julio is buying a car. He makes a down payment of 20% and he makes arrangements to finance the remaining $14,000. What is the dollar amount of Julio's down payment?

Answers

well, we know the downpayment is 20%, so 100% - 20% = 80%, that's the remaining amount, which we know is 14000 bucks, let's say the 20% is really "x" bucks, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 14000 & 80\\ x& 20 \end{array} \implies \cfrac{14000}{x}~~=~~\cfrac{80}{20} \\\\\\ \cfrac{ 14000 }{ x } ~~=~~ 4\implies 14000=4x\implies \cfrac{14000}{4}=x\implies 3500=x[/tex]

Someone help fast please

Find the value of sin
W rounded to the nearest hundredth, if necessary.

Answers

Answer:

30 i believe

Step-by-step explanation:

In ΔRST, r = 71 cm, � m∠T=48° and � m∠R=37°. Find the length of t, to the nearest 10th of a centimeter.

Answers

Answer:

t/sin T = r/sin R

where T and R are the measures of the opposite angles of t and r, respectively.

First, we need to find the measures of T and R in radians:

T = 48° * pi/180 = pi/4

R = 37° * pi/180 = 37 * pi/180

Next, we can use these values in the formula:

t/sin T = r/sin R

t = r * sin T / sin R

t = 71 * sin(pi/4) / sin(37 * pi/180)

Using a calculator, we can estimate t to the nearest 10th of a centimeter:

t ≈ 107.9 cm

So the length of t is approximately 107.9 cm to the nearest 10th of a centimeter.

Answer:87.7

Step-by-step explanation:

Determine whether the statements are true or false.
if a system of m linear equations in n variables is equivalent to a system of p linear equations in q variables, then m = p.

Answers

True, equivalent systems of linear equations always have the same number of variables (you can never reduce the number of variables and keep an equivalent system).

If a system of m linear equations in n variables is equivalent to a system of p linear equations in q variables, then m = p is true then.

Number of variables = number of columns in the matrix.

Cramer's rule is one of the important methods applied to solve a system of equations. In this method, the values of the variables in the system are to be calculated using the determinants of matrices. Thus, Cramer's rule is also known as the determinant method.

Cramer's rule can only be applies if

1.the number of equations in the linear system equals the number of variables i.e m = n.

2.the determinant of the coefficient matrix is non zero.

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a biologist is studying the depths of plants growing near the surface of the ocean he uses negeitive numbers to represent the depths of the plants he finds below sea level.the table shows the depths of four plants order the number from least to greatest

Answers

a) The data in ascending Order; -83/4 < -67/4 < -62/4 < -1/4.

b) Sea Grass is the furthest the Surface of water.

What is Ascending Order?

Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.

Given that -20 3/4, -15 1/2, -14 3/4, -1/4

Now, the above fraction into Normal fraction;

-83/4, -31/2, -67/4, -1/4.

Now, Arranging the data in ascending Order;

-83/4 < -67/4 < -62/4 < -1/4.

b) Since Sea Grass is the furthest below the Surface of water.

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P=(prime numbers less than 20) and Q=(odd numbers less than 10) find PnQ​

Answers

The solutions are,  P= 2,3,5,7,11,13,17,19 & Q= 1,3,5,7,9

when, P=(prime numbers less than 20) and Q=(odd numbers less than 10)

What is number?

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here, we have,

P=(prime numbers less than 20)

and Q=(odd numbers less than 10)

so, P= 2,3,5,7,11,13,17,19

as, A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers.

now,

Q= 1,3,5,7,9

as, Odd numbers are whole numbers that cannot be divided exactly into pairs. Odd numbers, when divided by 2, leave a remainder of 1. 1, 3, 5, 7, 9, 11, 13, 15 … are sequential odd numbers.

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r packages include sample datasets. they also include reusable r functions and documentation about how to use the functions. 1 point true false

Answers

It is true that r packages include sample datasets. They also include reusable r functions and documentation about how to use the functions.

The r packages do contain reusable r functions and documentation about how to use the functions. Not only that but they also include the sample data sets and provide tests for checking the code that we have generated.

The r packages are distributed with fifteen base packages that include grid, method, compilers, base, datasets, tools, splines, graphics, stats, stats4, translations, utils, grDevices, parallel, and tcltk.

These r packages introduce simpler ways of the r code distribution and documentation.

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18
18°
χ
Find the missing side. Round to the nearest tenth.

Answers

The missing side of Right triangle will be 9.8.

What is meant by Trigonometric angles?

Angles in trigonometry are those determined by the ratios of the trigonometric functions. In trigonometry, the relationship between a triangle's angles and sides is studied. The angle value is between 0 and 360 degrees. Angles 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360° are significant in trigonometry.

A subfield of mathematics called trigonometry is concerned with the study of triangles. It is sometimes known by the colloquial term "trig." In trigonometry, mathematicians look at how triangles' sides and angles relate to one another.

We have,

Hypotenuse = 18 cm

Perpendicular = x cm

One of the angle = 33°

Using the Trigonometric angles,

[tex]$${Sin 33^{\circ}=\frac{\text { Perpendicular }}{\text { Hypotenuse }}$[/tex]

substitute the values in the above equation, we get

So, [tex]$${Sin} 33^0=\frac{x}{18}$[/tex]

simplifying the equation, we get

[tex]$$x=18 Sin 33^0$[/tex]

x = 9.8

The missing side is 9.8.

Therefore, the missing side of Right triangle will be 9.8.

The complete question is:

Find the missing side. Round to the nearest tenth.

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A triangle has an area of 4 3/4 square units. the base is 3 units, what is the height?
.

Answers

The required height of the triangle for 3 units base is 3.16 units.

How to find are of right angled triangle?

If a right triangle's height and hypotenuse are all that are known, we must first determine the base using the Pythagoras theorem before determining the triangle's area. After that, we may calculate its area using the formula 1/2 base height.

According to question:

We have,

Area of triangle = 4(3/4)square units., Base = 3 units.

= 19/4 square units.

We know that

Area = bh/2

19/4 = (3)h/2

h = 19/6

h = 3.16 units

Thus, required height is 3.16 units.

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Breyelle is planning on purchasing a new sports utility vehicle.

Answers

Answer:

Please type or attach a question to be answered. Currently, all you have is as a question is the statement "Breyelle is planning on purchasing a new sports utility vehicle."

24:56 basic ratio help help help

Answers

Answer:
The basic ratio of 24:56 is 3:7

a player rolls two fair six sided dice until the player rolls doubles. the probability of rolling doubles with one roll of two fair dice is 1/6, what is the probability that it takes 3 rolls until the player rolls doubles

Answers

The probability that it takes three rolls until the player rolls doubles is 25/216.

The probability of rolling doubles with one roll of two fair six-sided dice is 1/6.

The probability of an event is nothing but a number between 0 and 1, where zero shows the impossibility, and one shows the certainty.

First, determine the probability of rolls to obtain doubles in each roll.

Fails in the first roll:

P = 1 - 1/6 = 5/6

Fails in the second roll:

P = 1 - 1/6 = 5/6

In the third roll, the player rolls doubles, that is,

p = 1/6

Now, the probability of requiring 3 rolls until getting doubles will be:

= 5/6 × 5/6 × 1/6

= 25/216

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calculer les produit suivant en ecritures scientifiques puis les classer dans l'ordre croissant:
a) 25 000 x 280 b) 30 000 x 850
c) 72 000 x 90 d) 330 x 850 000

Answers

Answer:

c < a < b < d

Step-by-step explanation:

a) 25000 x 280, c'est 7000000
ou 7 * 10^6

b) 30000 x 850, c'est 25500000
ou 25.5 * 10^6

c) 72000 x 90, c'est 6480000
ou 6.48 * 10^6

d) 330 x 850,000, c'est 280500000
ou 280.5 * 10^6

On peut dire que l'ordre croissant est:
6.48 * 10^6 < 7 * 10^6 < 25.5 * 10^6 < 280.5 * 10^6

∴ c < a < b < d

Voilà

A rectangular building ha a bae that i 255ft long, 255 feet wide, and the building i 42 ft tall. Find the unit for the volume of the building

Answers

The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.

The volume of the building will be calculated by the formula -

Volume = length × breadth × height

Thus, keeping the value of each component of building in the formula to find the volume of the building.

Volume of building = 255 × 255 × 42

Performing multiplication on Right Hand Side of the equation to find the value of volume

Volume of building = 2,731,050 feet³

Therefore, the volume of the building is 2,731,050 feet³.

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The data below are the monthly average high temperatures for New York City. What is the median temperature?
40, 40, 48, 61, 72, 78, 84, 84, 76, 65, 54, 42

Answers

Based on the information above, the average temperature for New York City would be 61 or 65.

How to find the average temperature of New York?

To find the average temperature of New York we must find the average of the temperatures recorded in each month. Here is the mathematical procedure:

To find the median we must organize the data from the smallest to the largest and identify the value or values that are located in the middle, then the median would be: 61 or 65.

40, 40, 42, 48, 54, 61, 65, 72, 76, 78, 84, 84.

According to the above, the average temperature would be 61° or 65°.

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Select all the points in the solution set of the graph below.

Answers

Step-by-step explanation:

It's a the second one pick the second one

show that the given argument is invalid by giving values for the predicates p and q over the domain {a, b}. (a) ∀x (p(x) → q(x)) ∃x ¬p(x) ∴ ∃x ¬q(x) (b) ∃x (p(x) ∨ q(x)) ∃x ¬q(x) ∴ ∃x p(x)

Answers

The given argument is invalid by giving values for the predicates p and q over the domain = But both P(a) = p(b) = f There doesn’t exist any x, such that p(x) is true

What is Values?

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value. For illustration: If we take 45 into account. Here, the fourth digit is in the tens column.

Given,

fx( p(x) – a(x))

f.(p(x))

fx (a(x))

Let p(a)=T

P(b) = F

And a(a) = T

A(b) = T

So, p(a)=a(a)

=T

P(a) – a(b)

= T

And p(b)=T

So, f.(p(x)-a(x))

Fx(p(x))are T

But we have a (a) + A(b) =T

So, there doesn’t exist any x, such that (x) is true

Hence fX (a(x)) Doesn’t follow from the given statement.

This argument is include

b) fx(p(x) v a(x))

fx (a(x))

fx p(x)

Let P(a) = F

P(b) = F

And a(a) = F

A(b) = T

So, p(b) v a(b) = T

A(a) = F

= ft((x))

But both P(a) = p(b)

= f There doesn’t exist any x, such that p(x) is true

Hence fx p(x)) Dose’t follow from the given statements.

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in a survey, the planning value for the population proportion is p=*0.25. how large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.1? round your answer to next whole number.

Answers

Sample size of 385 should be taken. Rounding up to the next whole number, the required sample size would be 385. So, in order to provide a 95% confidence interval with a margin of error of 0.1 for the population proportion of 0.25, a sample size of 385 should be taken.

We can use the formula:

n = (Z^2 * p * (1-p)) / E^2

where:

Z is the z-score corresponding to the desired confidence level (for 95% confidence, Z = 1.96)

p is the estimated population proportion (p = 0.25)

E is the desired margin of error (E = 0.1)

Plugging in the values:

n = (1.96^2 * 0.25 * (1 - 0.25)) / 0.1^2

n = 384.16

we are attempting to gauge the populace extent with a room for mistakes of 0.1 and a certainty level of 95%.

To find the example size we want, we utilize an equation that considers the assessed populace extent (0.25), the ideal safety buffer (0.1), and the certainty level (95%). The recipe gives us a number that we gather together to the closest entire number. For this situation, the recipe lets us know that we want to test 385 individuals.

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A bank credit card charge interet at the rate of 25% per year,compounded monthly. If a enior in college charge 1100 to pay for college expene, and intend to pay it in one year, what will he have to pay?

Answers

The amount the college senior will have to pay in one year, given the interest charge and the amount paid, is $ 1, 408. 80

How to find the amount?

To find the amount, you need to use the future value formula. This would show the amount the college senior would pay in a year given what they spent on the credit card.

The monthly rate is:

= 25 % / 12

= 25 / 12 %

The amount the college senior will pay is:

= 1, 100 x ( 1 + 25 / 12 % ) ¹²

= $ 1, 408. 80

Note : The brackets are raised to the power of 12 because of the number of months in a year which is the amount of time till the college senior pays back.

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8. What is the equation of a polynomial function R with rational
coefficients that has a zero of 2 + √3 and -5i?

Answers

Sums of terms with the pattern k.[tex]x^{n}[/tex]—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5.

What is polynomial?A polynomial is a mathematical expression made up of coefficients multiplied by the sum of powers in one or more variables.A polynomial is a mathematical statement made up of coefficients and indeterminates that uses solely the operations addition, subtraction, multiplication, and powers of positive-integer variables. x2 4x + 7 is an illustration of a polynomial of a single indeterminate x. A polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation, such as the quadratic equation, cubic equation, etc. As an illustration, the polynomial 2x+5 has an exponent of 1. A polynomial is described as an expression made up of variables, constants, and exponents that are joined using mathematical operations like addition, subtraction, and multiplication.

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A construction company can purchase nails for $5 per pound and screws for $7 per dozen. How many pounds of nails and how many dozen screws can the company buy if their budget is at most $200?
a) Let x be the pounds of nails and let y be the dozens of screws. Write an inequality that would model this
situation.

Answers

The inequality for the model of the situation is 200 ≤ 5x + 7y.

What is system of inequality?

At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the answer of a linear inequality is the ordered pair that resolves all inequalities in the system.

Given that, let x be the pounds of nails and let y be the dozens of screws.

The equation for, nails for $5 per pound is given as:

5x

The equation for, screws for $7 per dozen is given as:

7y

If their budget is at most $200, then the inequality representing the nails and the screws is:

200 ≤ 5x + 7y

Hence, the inequality for the model of the situation is 200 ≤ 5x + 7y.

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After 10 days, 95% of a radioactive material has decayed
a) What is the half-life of the material?
b) How long will it take for there to be 15% of the original material left?

Answers

how can do braily app use

Answer:

Below

Step-by-step explanation:

a)   1/2^n   will show how much remains after 'n' halflives

95 % = .95

.95 = 1/2^n    log both sides to find n = .07400058

          so 10 days is .07400058 half lives

               10 / .0740058 = half life = 135.1 days

b)     .15 = 1/2^n   shows   n = 2.736 halflives

        2.736 halflives * 135.1 days/halflife = 369.8 days

Calculate the size of angle DAB.​

Answers

Answer:

25

Step-by-step explanation:

DAB=180-CBA

=180-155

=25

pls give brainliest if correct

Answer:

[tex]\angle DAB=25 \textdegree[/tex]

Step-by-step explanation:

We can use the Sum of Interior Angles formula to help us evaluate the size of angle DAB.

The formula for the Sum of Interior Angles is

[tex](n-2)*180[/tex]

where [tex]n[/tex] is the number of sides.

In this example we have 4 sides.

[tex](4-2)*180\textdegree\\2*180\textdegree=360\textdegree[/tex]

So the sum of all the interior angles in this shape must add up to 360°.

We are given 2 right angles and 1 additional angle. There are 4 angles total. Since we are given 3 we can evaluate the value of the 4th angle.

[tex]\angle A +\angle B +\angle C+\angle D=360 \textdegree[/tex]

[tex]360 \textdegree-\angle B -\angle C-\angle D=\angle A[/tex]

[tex]360\textdegree-90\textdegree-90\textdegree-155\textdegree=25\textdegree[/tex]

Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts? (1 point) f(x) = −2x − 1 x g(x) 2 2 4 6 6 10 Group of answer choices:
A.The function f(x) has a higher y-intercept.
B.The function g(x) has a higher y-intercept.
C.They both have the same y-intercept.
D.The relationship between y-intercepts cannot be determined.

Answers

The answer is the function f(x) has a higher y-intercept, the correct option is A.

What is the slope of a straight line?

A straight line of the form

y = mx + c

has its slope as 'm'

It is constant for a line. The more the slope is, the steeper the line is.

Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.

Given;

f(x) = −2x − 1 x

g(x) 2 2 4 6 6 10

Now by comparing the function to the slope-intercept form of a line we get;

The y-intercept of function f(x) is; -1

Also, the table for the function g(x) is given by;

        x           g(x)

        2            2

        4            6

        6           10

The function g(x) satisfies the equation;

g(x)= 2x-2

The y-intercept of the function g(x) is; -2

We know that:

 -1 > -2

Therefore, the slope answer will be f(x) is higher than the y-intercept of the function g(x).

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i record the age, paint color, engine size and cost of 243 used cars in an online car dealership. the number of variables i have recorded is ?

Answers

The number of variables you have recorded for each of the 243 used cars in an online car dealership is 4.

A variable is a characteristic or attribute of an object or a set of objects that can be measured or recorded. In this case, you have recorded the age, paint color, engine size, and cost of each of the 243 used cars. Each of these characteristics represents a separate variable.

For example, the age of a car is a variable that can be measured or recorded, and it provides information about the car's history and how long it has been in use. The paint color, engine size, and cost of each car are also variables that can be recorded, and they provide additional information about each car's unique characteristics.

In total, you have recorded 4 different variables for each of the 243 used cars, so the number of variables is 4.

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7t+10(5t+5)–10
can you help me with this question

Answers

Given the question:

7t+10(5t+5)-10

First, distribute:

7t+50t+50-10

Next, combine like terms (7t+50t and 50-10)

57t+40

This cannot be simplified further.

7t+10(5t+5)-10=

57t+40
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