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# Calculus I -- Fall 2017 -- midterm

**MATH 229 -- Fall 2017 -- 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.

$\bullet$ **1.** Three straight lines are shown below. Find the equation of one of them:

$\bullet$ **2.** Find the average rate of change for the function given by the following data:
$$\begin{array}{r|c}
x&y=f(x)\\
\hline
-1&0\\
0&2\\
1&3\\
2&-1\\
3&-2\\
4&0\\
\end{array}$$

$\bullet$ **3.** The graph of a function $f$ is given below. Find the equation of a line tangent to the graph at $(0,-1)$.

$\bullet$ **4.** Illustrate with plots (separately) functions with the following behavior: (a) $f(x)\to +\infty$ as $x\to 1$; (b) $f(x)\to -\infty$ as $x\to 2^+$; (c) $f(x)\to 3$ as $x\to -\infty$.

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

$\bullet$ **6.** The graph of function $f$ is given below. Sketch the graph of the derivative $f'$ in the space under the graph of $f$. Identify all important features of the graph.

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

$\bullet$ **8.** Find the derivative of the function $f(x)=\sin (x^3)$ at $x=1$.