Thoroughly investigate the graph of f (x) = e−x2 . Identify all important qualities, such as where the function is increasing, decreasing, concave up, and concave down. Also identify point(s) of inflection, extrema, intercepts, and provide graphs of f ′(x) and f ″(x). Be sure to justify all statements both graphically and analytically. Homework Help ✎
Solve f′(x) = 0 to locate the extrema and determine the increasing/decreasing intervals.
Solve f''(x) = 0 to determine points of inflection and the intervals of concavity.