Thoroughly investigate the graph of
To find INCREASING vs. DECREASING: Solve
To find CONCAVE UP vs. CONCAVE DOWN: Solve
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.