### Home > CALC > Chapter 7 > Lesson 7.4.2 > Problem 7-186

Thoroughly investigate the graph of and

*. Be sure to justify all statements*

*graphically*and

*analytically.*

To find INCREASING vs. DECREASING: Solve and

*.*

To find CONCAVE UP vs. CONCAVE DOWN: Solve

*and*

*.*

LOCAL MAXIMA happen where increasing changes to decreasing.

LOCAL MINIMA happen where decreasing changes to increasing.

POINTS OF INFLECTION happen where concavity changes.

To find the GLOBAL MAXIMUM: compare (endpoint) with

*(local maximum). The highest value wins.*

To find GLOBAL MINIMUM: compare

*(endpoint) with*

*(local minima). The lowest value wins.*