Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of f(4) − f(2)? ≤ f(4) − f(2) ≤

Step-by-step explanation:

Given

Required

Determine the minimum and maximum value of f(4) - f(2)

This question will be answered using the following mean value theorem.

In this case: and

So, we have:

Make f(4) - f(2), the subject:

From the given range:

We have that; f'(x) is at minimum at 4

So, the minimum of f(4) - f(2) is:

We have that; f'(x) is at maximum at 5

So, the maximum of f(4) - f(2) is:

Hence, the minimum and maximum values can be expressed as:

answer: x=60