CPM Homework Help : CALC Problem 5-25

Use the graphs of f ′(x) and g′(x) below to determine the x-values of all local minimums, maximums, and points of inflection. Homework Help ✎

Hint (a):

f(x) will be increasing where f '(x) is positive, and vice versa.
f(x) will be concave up where f '(x) has positive slopes, and vice versa.

Answer (a):

Local max at x = −1; f'(x) changes from positive to negative.
Inflection points at x = −0.5, 0, 0.5; f '(x) changes slope.
Local min at x = 1; f '(x) changes from negative to positive.

Hint (b):

See the hint in part (a).