Calculus I Dr. G Forum 4 - Derivatives and the shape of graphs Use the following steps to answer the following questions. Find the zeros of f [set f (x) = 0 and solve] Find the critical numbers of f [set f'(x) = 0 and solve] Find the critical points [plug the critical numbers into f (x)] Find local min/max [plug the critical numbers into f"(x)] Find the inflection point(s) of f [set f"(x) = 0 and solve, plug the solutions into f (x)] Determine the intervals of increase/decrease Determine the intervals of concavity Find extra points in the graph as needed Exercise 1 Let f (x) = x(x + 1)(x -2). Find the intervals of increase/decrease, local max/min, intervals of concavity and inflection points. Use them to sketch the graph of the function