Thread: 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) ≤ _______

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 , so...

Tonio

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.

Answers: 6 and 15
taking the anti-derivative also seemed to work.