# Math Help - Suppose that 2 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below.

1. ## Suppose that 2 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below.

Suppose that 2 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below.

______ ≤ f(6) - f(3) ≤ _______

2. Originally Posted by superduper1
Suppose that 2 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below.

______ ≤ f(6) - f(3) ≤ _______

1) On one side, as the derivative is positive, the function is monotone increasing...

2) On the other side, you have $\frac{f(6)-f(3)}{6-3}=f'(c)\,,\,\,c\in (3,6)$ , so...

Tonio

3. Originally Posted by superduper1
Suppose that 2 ≤ f '(x) ≤ 5 for all values of x. Complete the inequality below.

______ ≤ f(6) - f(3) ≤ _______
Thinking geometrically, it should be enough to just draw two triangles, for the minimum choose the gentle slope, for the maximum choose steep slope, base will be 3, height will be the value that goes in a blank.