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Home > CALC > Chapter 7 > 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.