Identify the maxima and minima of
Find CANDIDATES for maxima and minima by setting the first derivative equal to
Decide if each candidate is a maximum, minimum or neither. You could check for slope change by evaluating the 1st-derivative at points close to each candidate. You could evaluate each candidate in the 2nd-derivative. If the graph is concave up, it cannot have a local max. And vice versa.
Recall that maxima and minima are