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\Huge{Quiz 4}

TQS 211
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\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 $[4]$  $\displaystyle{\alpha(t)=-2t^2+\frac{6}{\sqrt{t}}-\frac{1}{t^3}}$ 
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\item $[4]$ $\displaystyle{\beta(x)=\sqrt{x}(x^3+x^{\frac{1}{2}})}$ 
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\item $[3]$ $\displaystyle{\gamma(y)=2^y+y^2-2}$ 
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\item $[3]$ $\displaystyle{\delta(x)=7\ln x +\pi e^x}$ 
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\item The cost function of a company is unknown but increasing production from 100 units to 101 units increased costs from \$1500 to \$1550.

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\item $[1]$ Estimate the marginal cost at 100 units.
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\item $[3]$ Find the linear function that will approximate the cost function for values near 100, that is, find the equation for the line tangent to the Cost function at 100.
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\item $[2]$ Use (b) to estimate the cost of producing 118 units.
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