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\begin{center}

\Huge{Polynomial \& Exponential Derivatives}\\
\end{center}

\normalsize
While working in a group make sure you:
\begin{packed_itemize}
\item Expect to make mistakes but be sure to reflect/learn from them!
\item Are civil and are aware of your impact on others.
\item Assume and engage with the strongest argument while assuming best intent.
\end{packed_itemize}

\begin{enumerate}

\item Use the properties discussed in class to find the following:

$$\displaystyle{\frac{d}{dx}(x^4-6x^2+4) \hspace{2in} \left( \frac{3}{4}x^8 +x^\pi\right)' }$$

\vspace{2in}

$$\displaystyle{\left(\left( \frac{1}{2}x\right)^5\right)' \hspace{2in} \frac{d}{dx}\left(\frac{x^2-2\sqrt{x}}{x}\right) }$$
\vspace{2in}

\item For what values of $x$ does the graph of $f(x)=x^4-6x^2+4$ have a horizontal tangent?

\newpage

%\item For each $f$ defined below, find $f'(x)$.

%$f(x)=x^4+2\sin(x)$  \hspace{2in} $f(x)=\cos(x)-\frac{5}{\sqrt[3]{x^7}}$ 

%\vspace{2in}

\item Consider $\alpha(x)=x^4+2e^x$. Find the equation of the line tangent to the graph of $\alpha$ at the point $(0,2)$.
\vskip 3in
%\item Find the line normal to the line you found in part (a) that also passes through the point $(0,2)$.


 
 
 \item At what point on the curve of $y=1+2e^x-3x$ is the tangent line parallel to the line $3x-y=5$?
 \vskip 2in
 \end{enumerate}





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