Refer to the graph below of $f^\prime(x)$, the derivative of some function $f(x)$.

1. Where is $f(x)$ increasing? How can you tell?

   Hint (a):

   Notice that this is the graph of $f^\prime(x)$, the slopes of $f(x)$, and $f(x)$ will increase where its slopes are positive.

2. Approximate the interval on which $f(x)$ is concave up. Justify your conclusion with the graph.

   Hint (b):

   

3. Is $f^{\prime\prime}(0)$ positive or negative? Explain how you know.

   Hint (c):

   $f^{\prime\prime}(x)$ represents the slopes of the given graph, $f^\prime(x)$. So look at the graph. Does it have a positive or a negative slope at $x = 0$?