### Home > CALC > Chapter Ch7 > Lesson 7.4.2 > Problem 7-186

7-186.

To find INCREASING vs. DECREASING: Solve *f* '(*x*) > 0 and *f* '(*x*) < 0.

To find CONCAVE UP vs. CONCAVE DOWN: Solve *f* ''(*x*) > 0 and *f* ''(*x*) < 0.

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 *f*(endpoint) with *f*(local maximum). The highest value wins.

To find GLOBAL MINIMUM: compare *f*(endpoint) with *f*(local minima). The lowest value wins.