### Home > CALC > Chapter 9 > Lesson 9.3.2 > Problem 9-95

9-95.

Thoroughly investigate the graph of *f* (*x*) = *e*^{−}^{x}^{2} . 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.