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\begin{document}

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\centerline{\textbf{\large Exam \#2 $\cdot$ Thursday, March 1, 2007}}
\vspace*{.2in}
MATH 124 $\cdot$ Calculus I $\cdot$ Section 26 $\cdot$ Fall 2008  \hspace*{0.5in} Name \hrulefill
\vspace*{0.2in}

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\textbf{Problem 1.}  The following graph has four input points labeled:

\includegraphics{figures/e2f1.eps}

\textbf{Part (a).}  At which of the four labeled points is $G(t)$
continuous?

\textbf{Part (b).}  At which of the four labeled points is $G(t)$
differentiable?

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\textbf{Problem 2.}  The following graph has five input points labeled:

\textbf{Part (a).}
At which of the five labeled points is $q(x)$ the greatest?
At which of the five labeled points is $q(x)$ the least?

\textbf{Part (b).}
At which of the five labeled points is $q'(x)$ the greatest?
At which of the five labeled points is $q'(x)$ the least?

\textbf{Part (c).}
At which of the five labeled points is $q''(x)$ the greatest?
At which of the five labeled points is $q''(x)$ the least?

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\textbf{Problem 3.}  Let $f(x)=x^2+4$.  Compute $f'(x)$ using the limit
definition of derivative.

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\textbf{Problem 4.}  Sketch a function $f(x)$ such that
$f(x) < 0$ everywhere,
$f'(x) < 0$ everywhere, and
$f'(x) > 0$ everywhere.

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\textbf{Problem 5.}  Let $f(x) = x^x$.  Numerically approximate $f'(2)$ using
difference quotients.  Use at least three successively smaller values of $h$.

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\textbf{Problem 6.}  On a mountain-climbing expedition, you find that the air
becomes cooler as you climb.  Let $y$ be your altitude above sea level,
measured in feet; let $H$ be the air temperature in degrees Fahrenheit.

\textbf{Part (a).} What are the units of $H'(y)$?

\textbf{Part (b).} What is the sign of $H'(y)$?

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\textbf{Problem 7.}  In a lab experiment, you have microorganisms growing
in a Petri dish.  The number $m$ of microrganisms, in millions, is a
function of time $t$ in days since the start of the experiment.  This
number is given by
$$
	m(t) = 4.1 e^{0.24t}.
$$
Find the rate of change in population on day 5 of the experiment.  In your
answer, please show units and include 3 significant figures.

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\textbf{Problem 8.}  Compute
$$
	\frac{d}{dx}\left(\frac{1}{x^{1/2}}\right).
$$

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\textbf{Problem 9.}  Compute
$$
	\frac{d}{dz}\left(\frac{z+1}{2z+1}\right).
$$

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\textbf{Problem 10.}  Compute
$$
	\frac{d}{dt} \left(e^{-rt} \sin(t)\right)
$$
where $r$ is a constant.

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\textbf{Problem 11.}  Compute
$$
	\frac{d}{dy} \left(\ln(2+2y+y^2)\right).
$$

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\end{document}
