Consider the function $\operatorname{f}\left( x \right)={{x}^{2}}{{e}^{x}}$. Find the $x$-coordi

Question

Consider the function $\operatorname{f}\left( x \right)={{x}^{2}}{{e}^{x}}$. Find the $x$-coordinate(s) of any max/min points, points of inflection and hence sketch the graph of the function.

Accepted Answer

Local maximum: $x=-2$. Local minimum: $x=0$. Points of inflection: $x=-2\pm\sqrt2$. Sketch shown in the solution.

Differentiation - Stationary Points and Points of Inflection

Differentiation - Stationary Points and Points of Inflection

Solution:

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