Bailey L. answered • 06/25/20

First-year Biophysics student at the Johns Hopkins University.

Critical points occur where f'(x) = y = 0. Therefore, we will have a critical point for x such that 3<x<4, 5<x<6, and 7<x<8. When x is between 3 and 4, the critical point is a local minimum because the derivative changes from negative to positive. The same holds true for when x is between 7 and 8. When x is between 5 and 6, the critical point is a local maximum because the derivative changes from positive to negative.