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# Calculus I -- Fall 2018 -- midterm

**MATH 229 -- Fall 2018 -- Midterm exam**

Name:_________________________ $\qquad$ 8 problems, 10 points each

- Write the problems in the given order, each problem on a separate page.
- Show enough work to justify your answers; make reference to theorems and definitions.

$\bullet$ **1.** Three straight lines are shown below. Find their slopes:

$\bullet$ **2.** Your location is recorded every half-hour, shown below. Estimate your velocity as a function of time.
$$\begin{array}{r|c}
\text{time, }x&\text{location, }y\\
\hline
0&20\\
.5&30\\
1&20\\
1.5&20\\
2&50\\
\end{array}$$

$\bullet$ **3.** Sketch, when possible, the graph of (a) a function that is continuous but not differentiable, (b) a function that is differentiable but not continuous, (c) a function with $f'(c)=0$ but no extreme point at $c$.

$\bullet$ **4.** Using one-sided limits, describe the behavior of the two functions sketched below:

$\bullet$ **5.** From the definition (look it up!), compute the derivative of $f(x)=-x^2+x$ at $x=1$.

$\bullet$ **6.** Sketch the graph of the derivative of the second function given in problem #4. Identify all important features of the graph.

$\bullet$ **7.** Find the derivative of the function $f(x)=\cos \sqrt{x}$.

$\bullet$ **8.** Find the derivative of the function $f(x)=e^{\sin x}$.