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Quiz 3 (Chapter 11)
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<h3>Name-<br>
Math 213, Fall 2016, Quiz - Review of Chapter 11</h3>
<ol>
<li>Consider the function $f(x,y)=34+8x+x^2+4y-2y^2$ 
(shown in the contour plot)

<ol type="a"><li>On the plot, sketch an arrow that points in 
the direction of the gradient of $f$ at the point with 
coordinates $(1,0)$.
<li>Find $\myv\grad f$.
<li>Evaluate $\myv\grad f$ at $(1,0)$.
<li>What is the rate of change of the function at $(1,0)$ in the direction
$\myv u=\langle -1,-1\rangle$
</ol>
<img src="0g/Q3cp.jpg" style="width:250px">


<li style="page-break-before:always">Consider the surface $f(x,y)=4+x^3-y^3-6xy$.
<ol type="a">
<li>Calculate $f_x$ and $f_y$.
<li>Find all possible  <b>critical points</b> for this function.
<li>Determine whether each critical point is a local and/or global maximum, a local and/or global minimum, or a saddle point. <b>For this part only</b>, you may use <i>Mathematica</i> to make a surface plot or a contour plot of the function.  If you do, turn in a print-out of your plot.
</ol>
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