Question

Suppose f(x) is continuous on [2,8] and −2≤f′(x)≤4 for all x in (2,8). Use the Mean Value Theorem to estimate f(8)−f(2).

Answer 1

Well, based on mean value theorem, we know that

f'(x*) = [ f(8)-f(2) ] / [ 8 - 2]

Answer 2

We we start with:

−2 ≤ [f(8)-f(2)] / (8-2) ≤ 4

Answer 3

yes but we aren't told what f(x) is equal to..

Answer 4

We don't need f(x).

Answer 5

We are solving for f(8)-f(2)

Answer 6

If we let a = f(8)-f(2) then we have
−2 ≤ a / (8-2) ≤ 4

Answer 7

this is the exact question

Answer 8

Do you want an exact answer or something? I have you an inequality and all you have to do is simplify it.