Question

Given f'(x) = (1 − x)(4 − x), determine the intervals on which f(x) is increasing or decreasing.

Answer 1

to the risk of sounding redundant.

notice, your critical points are 1 and 4, so you check the regions about, namely, do a first-derivative test on them, check the picture below.

Answer 2

The critical points are at x = 1 and x = 4 giving you the intervals (-inf, 1), (1, 4) and (4, inf).

By substituting x values in these 3 intervals, you can see that f'(x) is positive in the first and third intervals and negative in the second interval.

This means that f(x) is increasing in the first and third intervals and decreasing in the second interval.

The answer is D.