### Home > CALC > Chapter 5 > Lesson 5.1.3 > Problem 5-25

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 ✎

*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.

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.

See the hint in part (a).