Question

f(x)=x^3−9x

Over which interval does f have a positive average rate of change?

Choose 1 answer:

(Choice A)

[-4,-1]

(Choice B)

[-1,2]

(Choice C)

[-2,1]

(Choice D)

[-3,3]

Answer 1

Answer:[-4,-1]

Step-by-step explanation:

Answer 2

The interval does f have a positive average rate of change is [-4,-1] and this can be determined by using the formula of rate.

Given :

$\rm f(x) = x^3-9x$

The following steps can be used in order to determine the interval does f have a positive average rate of change:

Step 1 - Write the given function.

$\rm f(x) = x^3-9x$   --- (1)

Step 2 - Now, substitute the value of x from the option in the above equation in order to determine the correct option.

Step 3 - At x = -4 the equation (1) becomes:

f(-4) = -28

Step 4 - At (x = -1) the equation (1) becomes:

f(-1) = 8

Step 5 - Now, the average rate of change is given below:

$\rm Rate = \dfrac{8+28 }{-1+4}$

Rate = 12

So, the correct option is A).

Form orte information, refer to the link given below:

https://brainly.com/question/5245372