# Math Help - Applications of Differentiation

1. ## Applications of Differentiation

Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below.

____________ ≤ f(6) - f(2) ≤ ____________

2. Hello,

Is that all you have ?

3. Originally Posted by topher0805
Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below.

____________ ≤ f(6) - f(2) ≤ ____________
$f(6)-f(2) = f'(c)(6-2)\implies 16\leq f(6)-f(2)\leq 20$. By the Mean Value Theorem.
(Here $c\in (2,6)$).

4. Thanks for the help.

Just to clarify, since 6-2 is 4, you multiplied both sides of the original inequality by 4 so that you had f(6)-f(2) by itself in the middle?

5. Originally Posted by topher0805
Thanks for the help.

Just to clarify, since 6-2 is 4, you multiplied both sides of the original inequality by 4 so that you had f(6)-f(2) by itself in the middle?
Exactly. you are on your way to be a math professor.