Science:Math Exam Resources/Courses/MATH102/December 2013/Question C 03/Statement

Consider the function

$f(x)=x^2{e}^{-x}$

defined on the whole real line.

Find all zeros of $f,f^{\prime }$ and $f^{″}$ and determine all local minima, maxima and inflection points of f. Sketch the graph of f. You may use the fact that $\underset{x\to \mathrm{\infty }}{\lim }{x}^2{e}^{-x}=0$.