At which point(s) on the graph of $y = f(x)$ at right, do the following situations occur?

1. $f^\prime(x)$ and $f^{\prime\prime}(x)$ are both positive

   Hint (a):

   Translation: slope of $f\left(x\right)$ is positive AND $f\left(x\right)$ is concave up.

2. $f^\prime(x)$ and $f^{\prime\prime}(x)$ are both negative

   Hint (b):

   Refer to the hint in part (a).

3. $f^\prime(x)$ is positive and $f^{\prime\prime}(x)$ is negative

   Hint (c):

   Refer to the hint in part (a).

4. $f^\prime(x)$ is negative and $f^{\prime\prime}(x)$ is positive

   Answer (d):

   Points $e$ and $a$.