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\title{Math 103, Fall 2014}
\author{Quiz on Week 5 Material}

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\hfill{\bf Name: } $\underline{\hspace{2.7in}}_{\mbox{}}$

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What value should the constant $c$ have so that
\[f(x)=\left\{\begin{array}{ll}
\frac{x-1}{e^x}&\text{if }x\leq 1\\
c(x-1)e^x&\text{if }x>1\\
\end{array}\right.\]
is differentiable everywhere?

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The product and quotient rules are:
\[\frac{d}{dx}[u\cdot v]=u\frac{dv}{dx}+v\frac{du}{dx}\ \text{ and }\ \frac{d}{dx}(\frac{u}{v})=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}.\]

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