4. Let $f$ be a function defined on the closed interval $- 3 \leq x \leq 4$ with $f ( 0 ) = 3$. The graph of $f ^ { \prime }$, the derivative of $f$, consists of one line segment and a semicircle, as shown above. (a) On what intervals, if any, is $f$ increasing? Justify your answer. (b) Find the $x$-coordinate of each point of inflection of the graph of $f$ on the open interval $- 3 < x < 4$. Justify your answer. (c) Find an equation for the line tangent to the graph of $f$ at the point ( 0,3 ). (d) Find $f ( - 3 )$ and $f ( 4 )$. Show the work that leads to your answers. [Figure]
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4. Let $f$ be a function defined on the closed interval $- 3 \leq x \leq 4$ with $f ( 0 ) = 3$. The graph of $f ^ { \prime }$, the derivative of $f$, consists of one line segment and a semicircle, as shown above.\\
(a) On what intervals, if any, is $f$ increasing? Justify your answer.\\
(b) Find the $x$-coordinate of each point of inflection of the graph of $f$ on the open interval $- 3 < x < 4$. Justify your answer.\\
(c) Find an equation for the line tangent to the graph of $f$ at the point ( 0,3 ).\\
(d) Find $f ( - 3 )$ and $f ( 4 )$. Show the work that leads to your answers.\\
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