Generate Math Exams and Quizzes in LaTeX and pdf formats

The difference quotient is \(\displaystyle \frac{f(x+h)-f(x)}{h}\). Evaluating \(\displaystyle f(x+h)=- 8 h - 8 x + 8 \left(h + x\right)^{3} + 3 \left(h + x\right)^{2} - 9\) and expanding gives \(\displaystyle f(x+h)=8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h + 8 x^{3} + 3 x^{2} - 8 x - 9\) Evaluating the difference quotient gives \(\displaystyle \frac{(8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h + 8 x^{3} + 3 x^{2} - 8 x - 9)-(8 x^{3} + 3 x^{2} - 8 x - 9)}{h}\) Simplifying gives \(\displaystyle \frac{8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h}{h}=8 h^{2} + 24 h x + 3 h + 24 x^{2} + 6 x - 8\)

Download \(\LaTeX\)

\begin{question}Find the difference quotient of $f(x)=8 x^{3} + 3 x^{2} - 8 x - 9$ . 
    \soln{9cm}{The difference quotient is $\frac{f(x+h)-f(x)}{h}$. Evaluating $f(x+h)=- 8 h - 8 x + 8 \left(h + x\right)^{3} + 3 \left(h + x\right)^{2} - 9$ and expanding gives $f(x+h)=8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h + 8 x^{3} + 3 x^{2} - 8 x - 9$  Evaluating the difference quotient gives $\frac{(8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h + 8 x^{3} + 3 x^{2} - 8 x - 9)-(8 x^{3} + 3 x^{2} - 8 x - 9)}{h}$ Simplifying gives $\frac{8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h}{h}=8 h^{2} + 24 h x + 3 h + 24 x^{2} + 6 x - 8$ }

\end{question}

Download Question and Solution Environment\(\LaTeX\)

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}

\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}

\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}

\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue

\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}

HTML for Canvas

<p> <p>Find the difference quotient of  <img class="equation_image" title=" \displaystyle f(x)=8 x^{3} + 3 x^{2} - 8 x - 9 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3D8%20x%5E%7B3%7D%20%2B%203%20x%5E%7B2%7D%20-%208%20x%20-%209%20" alt="LaTeX:  \displaystyle f(x)=8 x^{3} + 3 x^{2} - 8 x - 9 " data-equation-content=" \displaystyle f(x)=8 x^{3} + 3 x^{2} - 8 x - 9 " />  . </p> </p>

HTML for Canvas

<p> <p>The difference quotient is  <img class="equation_image" title=" \displaystyle \frac{f(x+h)-f(x)}{h} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D%20" alt="LaTeX:  \displaystyle \frac{f(x+h)-f(x)}{h} " data-equation-content=" \displaystyle \frac{f(x+h)-f(x)}{h} " /> . Evaluating  <img class="equation_image" title=" \displaystyle f(x+h)=- 8 h - 8 x + 8 \left(h + x\right)^{3} + 3 \left(h + x\right)^{2} - 9 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%2Bh%29%3D-%208%20h%20-%208%20x%20%2B%208%20%5Cleft%28h%20%2B%20x%5Cright%29%5E%7B3%7D%20%2B%203%20%5Cleft%28h%20%2B%20x%5Cright%29%5E%7B2%7D%20-%209%20" alt="LaTeX:  \displaystyle f(x+h)=- 8 h - 8 x + 8 \left(h + x\right)^{3} + 3 \left(h + x\right)^{2} - 9 " data-equation-content=" \displaystyle f(x+h)=- 8 h - 8 x + 8 \left(h + x\right)^{3} + 3 \left(h + x\right)^{2} - 9 " />  and expanding gives  <img class="equation_image" title=" \displaystyle f(x+h)=8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h + 8 x^{3} + 3 x^{2} - 8 x - 9 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%2Bh%29%3D8%20h%5E%7B3%7D%20%2B%2024%20h%5E%7B2%7D%20x%20%2B%203%20h%5E%7B2%7D%20%2B%2024%20h%20x%5E%7B2%7D%20%2B%206%20h%20x%20-%208%20h%20%2B%208%20x%5E%7B3%7D%20%2B%203%20x%5E%7B2%7D%20-%208%20x%20-%209%20" alt="LaTeX:  \displaystyle f(x+h)=8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h + 8 x^{3} + 3 x^{2} - 8 x - 9 " data-equation-content=" \displaystyle f(x+h)=8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h + 8 x^{3} + 3 x^{2} - 8 x - 9 " />   Evaluating the difference quotient gives  <img class="equation_image" title=" \displaystyle \frac{(8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h + 8 x^{3} + 3 x^{2} - 8 x - 9)-(8 x^{3} + 3 x^{2} - 8 x - 9)}{h} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B%288%20h%5E%7B3%7D%20%2B%2024%20h%5E%7B2%7D%20x%20%2B%203%20h%5E%7B2%7D%20%2B%2024%20h%20x%5E%7B2%7D%20%2B%206%20h%20x%20-%208%20h%20%2B%208%20x%5E%7B3%7D%20%2B%203%20x%5E%7B2%7D%20-%208%20x%20-%209%29-%288%20x%5E%7B3%7D%20%2B%203%20x%5E%7B2%7D%20-%208%20x%20-%209%29%7D%7Bh%7D%20" alt="LaTeX:  \displaystyle \frac{(8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h + 8 x^{3} + 3 x^{2} - 8 x - 9)-(8 x^{3} + 3 x^{2} - 8 x - 9)}{h} " data-equation-content=" \displaystyle \frac{(8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h + 8 x^{3} + 3 x^{2} - 8 x - 9)-(8 x^{3} + 3 x^{2} - 8 x - 9)}{h} " />  Simplifying gives  <img class="equation_image" title=" \displaystyle \frac{8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h}{h}=8 h^{2} + 24 h x + 3 h + 24 x^{2} + 6 x - 8 " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B8%20h%5E%7B3%7D%20%2B%2024%20h%5E%7B2%7D%20x%20%2B%203%20h%5E%7B2%7D%20%2B%2024%20h%20x%5E%7B2%7D%20%2B%206%20h%20x%20-%208%20h%7D%7Bh%7D%3D8%20h%5E%7B2%7D%20%2B%2024%20h%20x%20%2B%203%20h%20%2B%2024%20x%5E%7B2%7D%20%2B%206%20x%20-%208%20" alt="LaTeX:  \displaystyle \frac{8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h}{h}=8 h^{2} + 24 h x + 3 h + 24 x^{2} + 6 x - 8 " data-equation-content=" \displaystyle \frac{8 h^{3} + 24 h^{2} x + 3 h^{2} + 24 h x^{2} + 6 h x - 8 h}{h}=8 h^{2} + 24 h x + 3 h + 24 x^{2} + 6 x - 8 " />  </p> </p>