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Questions: Algebra BusinessCalculus
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Find the derivative of \(\displaystyle f(x)=14 x^{3} - 13 x^{2} - 5 x - 19\).
Using the power rule gives \(\displaystyle f'(x)=42 x^{2} - 26 x - 5\).
\begin{question}Find the derivative of $f(x)=14 x^{3} - 13 x^{2} - 5 x - 19$. \soln{9cm}{Using the power rule gives $f'(x)=42 x^{2} - 26 x - 5$. } \end{question}
\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}
<p> <p>Find the derivative of <img class="equation_image" title=" \displaystyle f(x)=14 x^{3} - 13 x^{2} - 5 x - 19 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3D14%20x%5E%7B3%7D%20-%2013%20x%5E%7B2%7D%20-%205%20x%20-%2019%20" alt="LaTeX: \displaystyle f(x)=14 x^{3} - 13 x^{2} - 5 x - 19 " data-equation-content=" \displaystyle f(x)=14 x^{3} - 13 x^{2} - 5 x - 19 " /> . </p> </p>
<p> <p>Using the power rule gives <img class="equation_image" title=" \displaystyle f'(x)=42 x^{2} - 26 x - 5 " src="/equation_images/%20%5Cdisplaystyle%20f%27%28x%29%3D42%20x%5E%7B2%7D%20-%2026%20x%20-%205%20" alt="LaTeX: \displaystyle f'(x)=42 x^{2} - 26 x - 5 " data-equation-content=" \displaystyle f'(x)=42 x^{2} - 26 x - 5 " /> . </p> </p>