I have a question on the application of defferentiation?

Question

Suppose that 3 ≤ f’(x) ≤ 5 for all values of x. Show that 18 ≤ f(8) – f(2) ≤ 30.

Answer 1

You probably have not copied the problem correctly. First there is nothing about derivatives in your question. Second, Since f(x) is always between 3 and 5 the maximum difference between two vaues of f(x) would be 5-3= 2.

Answer 2

Integrate all three components of the inequality with respect to x, from x=2 to x=8.