Question

Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x = 2. There are horizontal tangents at x = -1.5 and x = 1.5. Which of the following statements is true?

f has a relative minimum at x = 1.5.
f has a relative maximum at x = -1.5.
f is decreasing on the interval from x = 1 to x = 2.
None of these is true.

Thank you in advance!

Answer 1

f is decreasing on the interval from x = 1 to x = 2.

Explanation:

f has a relative minimum when f' changes signs from - to +.

f has a relative maximum when f' changes signs from + to -.

f is decreasing when f' is negative.

f' is not changing signs at x=-1.5 or x=1.5, so neither of these are minimums or maximums of f. However, f does have relative minimums at x=-3 and x=2, and a relative maximum at x=1

f' is negative between x=1 and x=2. So f is decreasing in this interval.