CPM Homework Help : APCALC Problem 4-153

The graph of $y = f^\prime\left(x\right)$ is shown at right. Determine the intervals where $f$ is increasing, decreasing, concave up, and concave down.

hint:

We are looking at a graph of $f^\prime\left(x\right)$ , but being asked about the graph of $f\left(x\right)$ .
So think about what $f^\prime\left(x\right)$ tells us about $f\left(x\right).$

Hint:

If $f^\prime\left(x\right)$ is positive, then $f\left(x\right)$ is increasing (and vice versa).
If $f^\prime\left(x\right)$ is increasing, then $f\left(x\right)$ is concave up (and vise versa).

Continuous curve labeled, f prime of x, coming from lower left, turning at the approximate points (negative 1, comma 3), & (3, comma negative 0.5), passing through the x axis at negative 3, 2, & 4, changing from concave down to concave up at about (1, comma 1).