### Home > CALC > Chapter 9 > Lesson 9.3.2 > Problem9-95

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 $f^\prime(x)$ and $f^{\prime\prime}(x)$. Be sure to justify all statements both graphically and analytically.

Solve $f^\prime(x) = 0$ to locate the extrema and determine the increasing/decreasing intervals.
Solve $f^{\prime\prime}(x) = 0$ to determine points of inflection and the intervals of concavity.