The graph below shows the graph of the derivative of $f(x)$. Give approximate answers to the questions below and justify your responses.

1. a. For what values of $x$ in the interval $[−4, 4]$ does $f$ attain a relative minimum?

   Hint (a):

   This occurs when $f^\prime(x)$, or the slope function, changes from negative to positive.

2. At what value of $x$ does a critical point that is neither a relative maximum nor a relative minimum exist?

   Hint (b):

   This occurs when $f^\prime(x) = 0$, but does not change from negative to positive.

3. For what values of $x$ in the interval $[−4, 4]$ is the graph of $f$ concave up?

   Hint (c):

   This occurs when $f^\prime(x) = 0$.