Question

Question: Suppose that 4 <= f'(x) <= 5 for all values of x. How do I prove that:

16 <= f(6) - f(2) <= 20

Answer 1

Use the mean value theorem: \[f(b) - f(a) = f'(c)(b-a),\]
where \(c\) is some number between 2 and 6.