Use the graph of $f^\prime(x)$ below to answer the following questions.

1. At what $x$-value(s) does $f(x)$ have a relative minimum?

   Hint (a):

   This occurs when $f(x)$ changes from negative to positive.

2. Where does $f(x)$ have a point of inflection?

   Hint (b):

   This occurs when the slope of $f^\prime(x)$ is $0$.

3. Describe what happens on the graph of $f^{\prime\prime}(x)$ when $x = 5$.

   Hint (c):

   What is the slope of the given graph at $x = 4.8$?
   At $x = 5$?
   At $x = 5.2$?

4. Describe the graph of $f(x)$ when $x = 0$.

   Hint (d):

   Review your answer to part (b).

5. If $f(0) = 2$ , estimate $f(3)$.

   Hint (e):

   $f(3)=f(0)+\int_0^3f^\prime(x)dx$