Question

If f(3) = 12 and f '(x) ≥ 3 for 3 ≤ x ≤ 5, how small can f(5) possibly be?

Answer 1

18

Explanation:

Since f '(x) ≥ 3, that means for every x, it can increase by 3 or greater. If we want to find the smallest f(5), we have to use the smallest rate of change possible, which is just 3.

Then, we have to find how many times x changes. Since we are going from 3 to 5, that means x changes 2 times. (5 - 3 = 2)

Now we multiply the rate of change (3) by the number of x changes.

3 x 2 = 6

We then add that to 12 since that is the number we started with

12 + 6 = 18