% TEMPLATE FOR STANDARD QUIZ
% by laura
\documentclass[14pt,epsfig]{article}

\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{hyperref}
\oddsidemargin=0in
\evensidemargin=0in
\textwidth=6.3in
\topmargin=-0.5in
\textheight=9in

\parindent=0in
\pagestyle{empty}

%testpoints.tex
\oddsidemargin=0in
\evensidemargin=0in
\textwidth=6.3in
\topmargin=-0.5in
\textheight=9in
\parindent=0in
\pagestyle{empty}

\newcounter{problemnum}
\renewcommand{\theproblemnum}{\arabic{problemnum}}
\newcounter{partnum}[problemnum]
\renewcommand{\thepartnum}{\alph{partnum}}
\newcounter{totalpoints}
\newcounter{curprobpts}	
\newcounter{totalparts}
\newcounter{pagepoints}
\newenvironment{problem}[1]{
\refstepcounter{problemnum}
\vspace{0.15in} \par
\setcounter{curprobpts}{#1} \setcounter{totalparts}{0}
{\Large \bf \theproblemnum. \normalsize ({\it \arabic{curprobpts} point\null\ifnum \value{curprobpts} = 1\else s\fi}\/)}
}{\ifnum \value{totalparts} = 0
	\addtocounter{totalpoints}{\value{curprobpts}}	% Add pts to total.
	\addtocounter{pagepoints}{\value{curprobpts}}
	\else \ifnum \value{totalparts} = \value{curprobpts}
	\else \typeout{}
	\typeout{!!!!!!!   POINT ACCOUNTING ERROR   !!!!!!!!}
	\typeout{PROBLEM [\theproblemnum] WAS ALLOCATED \arabic{curprobpts} POINTS,}
	\typeout{BUT CONTAINS PARTS TOTALLING \arabic{totalparts} POINTS!}
	\typeout{}
	\fi
\fi
}
\newcommand{\newpart}[1]
{
\refstepcounter{partnum}
\hspace{0.25in}	
\ifnum #1 > 0
	\makebox[0.5in][l]{{\bf \thepartnum.} {\bf ({\it #1 pt\ifnum #1 = 1\else s\fi\/}) \,\,}}
\else
	\makebox[0.25in][l]{({\bf \thepartnum})}
\fi
\hspace{0.1in}	
\addtocounter{totalparts}{#1}
\addtocounter{pagepoints}{#1}
\addtocounter{totalpoints}{#1}
}
\newcommand{\skipproblem}[1]{\addtocounter{problemnum}{#1}}

\newcommand{\showpoints}
{
\typeout{}  
\typeout{====> A TOTAL OF \arabic{totalpoints} POINTS WERE READ.}
\typeout{}
}
%%%%%end testpoints.tex
%\input{testpoints}

\begin{document}


%%%(change to appropriate class and semester)
MATH 2222HJ Spring 2016

%%%(change to appropriate quiz type and date)
Quiz 4 \hspace{1.9in} {Name:} {\underline {\hspace{2.5in}}}
\vspace{2pc}

%%%(modify rules, time, points as appropriate)
Show all work clearly and in order, and circle your final answers.  

Justify your answers algebraically whenever possible. Unjustified work may not receive full credit.
\vspace{2pc}

\begin{problem}{2}
Suppose that $f(x,y,z)=3yze^{2x}$ and $x=2t$, $y=4t$, and $z=\sin(2t)$. Compute $\dfrac{\mathrm{d}f}{\mathrm{d}t}$ whenever $t=\dfrac{\pi}{2}$.
\vfill
\end{problem}

\vfill
\begin{problem}{3}
Consider the function $f(x,y)=6x^2+4xy-3y^2$ and the point $P=(6,-1)$. Find the direction of steepest ascent at $P$ and find a vector that points in the direction of no change at $P$.
\vfill
\end{problem}

\vfill
\showpoints
\end{document}