The function f is given by f(x)=(x^{3}+bx+6)(g(x)), where b is a constant and g is a differentiable function satisfying g(2)=3 and g′(2)=−1. For what value of b is f′(2)=0?

7
10
12
22

Answers

Answer 1

Answer:

[tex]\displaystyle b = -22[/tex]

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = (x^3+bx+6)(g(x))[/tex]

Where b is a constant and g is a differentiable function.

And we want to determine the value of b such that f'(2) = 0.

Find f' using the product rule:

[tex]\displaystyle \begin{aligned} f'(x) & = \frac{d}{dx}\left[ (x^3+bx+6)(g(x))\right] \\ \\ & = \frac{d}{dx}\left[ x^3 + bx + 6\right] g(x) + (x^3+bx+6)\frac{d}{dx}\left[ g(x)\right] \\ \\ & = (3x^2+b)(g(x)) + (x^3 + bx + 6)(g'(x))\end{aligned}[/tex]

Substitute using known values and solve for b:

[tex]\displaystyle \begin{aligned}f'(2) = 0 & = (3(2)^2+b)(g(2)) + ((2)^3+b(2)+6)(g'(2)) \\ \\ 0 & = (12+b)(3) + (14+2b)(-1) \\ \\ 0 & = 22 +b \\ \\ b & = -22\end{aligned}[/tex]

In conclusion, the value of b is -22.

Answer 2

The function f is given b is a constant and g is a differentiable function the value b (-8.4),

Let's start by finding the derivative of the given function f(x) with respect to x:

f(x) = (x³ + bx + 6) × g(x)

Using the product rule for differentiation, the derivative of f(x) is:

f'(x) = (x³ + bx + 6) × g'(x) + g(x) × (3x² + b)

Now we are interested in finding the value of b for which f'(2) = 0. So, let's plug in x = 2 and use the information given about g(2) and g'(2):

f'(2) = (2³ + 2b + 6) × g'(2) + g(2) × (3 × 2² + b)

Since g(2) = 3 and g'(2) = -1,

f'(2) = (8 + 2b + 6) × (-1) + 3 × (3 × 4 + b)

= (2b + 14 - 8) + 3× (12 + b)

= 2b + 6 + 36 + 3b

= 5b + 42

Now, we want to find the value of b for which f'(2) = 0:

5b + 42 = 0

Subtracting 42 from both sides:

5b = -42

Dividing both sides by 5:

b = -8.4

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Complete question:

The function f is given by f(x)=(x^{3}+bx+6)(g(x)), where b is a constant and g is a differentiable function satisfying g(2)=3 and g′(2)=−1. For what value of b is f′(2)=0?

7

10

12

22

-8.4


Related Questions

squared root of -100 =

Answers

10 i I hope this help

Step-by-step explanation:

Please this is a wrong question. If you mean square root of 100 then it's 10. As for -100, it's an error.

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Answers

Step-by-step explanation:

the distance between 2 points can be seen as the Hypotenuse of a right-angled triangle with the legs being the x and y coordinate differences.

and so, we use Pythagoras

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Laurie wants to join the basketball team. Her parents ask her to figure out how much it will cost. Laurie knows that she has to pay an activities fee of $42 plus a fixed amount for each tournament. Write a formula that describes how much it will cost to join the team. Let's let:

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The Formula:

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Alicia sold 59 fewer tickets than Jenna and Matt sold together. How many tickets did Alicia sell ? Explain

Answers

Answer:

I'm guessing 401 tickets. lol

Number of tickets Alicia sold is equals to 401 .

What is linear equation?

" Linear equation is defined as the algebraic expression with one or more variables with highest power of the variable equals to one."

According to the question,

x represents the number of tickets Alicia sold

As per the data given,

Number of tickets Jenna and Matt sold together = 282 + 178

                                                                                 = 460 tickets

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The ordered pair (8,2) is found in the ____ Quadrant

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The first quadrant (quadrant I) =]

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Answers

The equation used to model the regular cost of each chair at Maplewood Furniture store is given by 6c - 55 = 455

A linear equation is in the form:

y = mx + b;

where y, x are variables, m is the rate of change and b is the y intercept.

Let c represent the regular cost for x chairs. Hence:

c = mx + b

Given that a discount of $55 is applied to the total, hence, b = -55.

Rhianna buys a set of 6 chairs and pays 455, hence:

6c - 55 = 455

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The equation is given by 6c - 55 = 455 and the regular cost of each chair is $85

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Answers

Answer:

5(37)+10

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Step-by-step explanation:

5x+10=180

-10 -10

5x=170

divide by 5

x=37

---------------------

10x+5=180

-5 -5

10x=175

divide by 10

x=17.5

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

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Step-by-step explanation:

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Hope that helps

Answer:

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Step-by-step explanation:

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Which equation is correct?

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Answers

D is the correct answer

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How to determine the correct expression?

The product expression is given as:

235 * 8

Express 235 as place values

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Expand the bracket

235 * 8 = 200 * 8 + 30 * 8 + 5 * 8

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Answers

Answer:

Step-by-step explanation:

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Here are 2 examples

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y = 3x + 19

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Their range is - infinity <y < + infinity.

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Answers

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Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

16/125

Step-by-step explanation:

Write 0.128 as

0.128/1

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

??

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

becuase b is bad for you

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Answers

Answer:

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Step-by-step explanation:

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WILL GIVE BRAINLYIEST   Rita goes to the mall. If x is the number of items she ​bought, the expression 18.54x+23 gives the amount she spent in dollars at one store. Then she spent 25 dollars at another store. Find the expression which represents the amount Rita spent at the mall. Then estimate how much Rita spent if she bought 2 items.

Answers

I only know the first part (the expression which represents the amount Rita spent at the mall)

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Answers

Answer:

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Step-by-step explanation:

This can also be written like this.

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

can you give more context to the question and I will answer it in the comments? thanks!

Answer:

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Step-by-step explanation:

Question : Explore criteria of congruency of triangles using a set of triangle cut outs

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Answer:

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Answer:

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