Use the graph of f '(x) below to find the x-values of the relative minimum on the graph of f(x):

Question

Use the graph of f '(x) below to find the x-values of the relative minimum on the graph of f(x):

1. A: 0.5

1. B: 2 and 0

1. C: 1

1. D: 1.5

Answer 1

In the minimum point x0:

f'(x0) = 0, and around x0 f'(x) < 0 for x < x0 and f'(x) > 0 for x > x0. Only points x = 0 and x = 2 satisfy this conditions. Hence, B is the correct answer.