\section*{Homework 2}\label{p1hw1}

Find all the location of the critical points, within the given domain, of the following functions:
\begin{enumerate}
\item $f(x)=x\ln (x)$ for $x\geq 0$.
\item $f(x)=x^2e^{-x}$ for all real $x$, i.e., $-\infty<x<\infty$.
\item $f(t)=3t^5-18t^4-5t^2+7t-15$ for all real $t$ (\textbf{Hint:} use Mathematica).
\item $H(\theta)=\theta\cos(5\theta)$ for $\theta\in[-\pi,\pi]$.
\end{enumerate}
Questions 1 and 4 will be graded. 