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

• Jul 22nd 2010, 05:30 PM
superduper1
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) ≤ _______
• Jul 22nd 2010, 06:14 PM
tonio
Quote:

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 $\displaystyle \frac{f(6)-f(3)}{6-3}=f'(c)\,,\,\,c\in (3,6)$ , so...

Tonio
• Jul 22nd 2010, 06:41 PM
undefined
Quote:

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.
• Jul 27th 2010, 03:46 PM
superduper1