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 $\displaystyle f,f'$ and $\displaystyle f''$ and determine all local minima, maxima and inflection points of f. Sketch the graph of f. You may use the fact that $\lim _{x\to \infty }x^{2}e^{-x}=0$.