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	Name: \hrulefill & & Math 1441 Quiz 3 \\[0.2cm]
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\noindent\textbf{1.} (8 pts) The graph of $f$ is given on the left. Sketch the graph of $f'$ on the right.\\

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	\includegraphics[scale=0.5]{quiz3-2.png}
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\noindent\textbf{2.} (6 pts) The graph below shows the temperature of a city between 6 A.M. and 6 P.M.

(1) At what time does the temperature increases most rapidly?

(2) At what time does the temperature decreases most rapidly?\\

\includegraphics[scale=0.5]{quiz3-3.png}

\noindent\textbf{3.} Let $f(x)=x^2$.

(1) (2 pts) Sketch the graphs of $f$.

(2) (2 pts) Sketch the graphs of $f'$ based on the graph of $f$.

(3) (2 pts) Find $f'(2)$ by using the definition $f'(x_0)\stackrel{\text{def}}{=}\lim\limits_{x\rightarrow x_0}\frac{f(x)-f(x_0)}{x-x_0}.$

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