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\Huge{Quiz 5}

TQS 211
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\normalsize
\noindent{You are welcome to use any written homework from Chapter 3, worksheets you completed, and a calculator but no books or class notes.  Show \emph{all} your work (algebraically or geometrically) for each and simplify. No credit is given without supporting work.}

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\item Find the derivative of the following functions:
 

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\item $[3]$  $\displaystyle{\alpha(t)=(t^2+3)e^t}$ %\S 3.4 \#8
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\item $[2]$ $\displaystyle{\beta(x)=5\sin (x)-5x+4}$ %\S3.5 \#6 
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\item $[4]$ $\displaystyle{\gamma(p)=p\ln(2p+1)}$ 
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\item If $f(x)=$, find $\displaystyle{f'(x)=\frac{6x^4-x^{\frac{1}{3}}}{\sqrt{x}}}$ in the following \emph{two} ways:
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\item $[3]$ by using the product or quotient rule
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\item $[3]$ by using precalculus to simplify first and using the power rule
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\item Simplify the above answers to make sure they are consistent with one another.
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\item Let $f$ and $g$ have the values in the following table:

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x &1 &0 &-2 &10 &12\\
\hline
$f(x)$ &0 &-2&0 &-792 & -1430\\
$g(x)$ &-2 &-2&10&178&262\\
$f'(x)$ &7 &3&-19&-259 &-383\\
$g'(x)$&2&-2&10&38&46\\
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\vspace{-1in}\item $[2]$ Find $\displaystyle{\left(\frac{f}{g}\right)' (1)}$.
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\item $[3]$ Find $(f\circ g)' (0)$.
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