CPM Homework Help : APCALC Problem 4-123

Refer to the graph at right of $y = f^\prime\left(x\right)$ , the derivative of some function $f$ .

Where is $f$ increasing? How can you tell?
Hint (a):
Notice that this is the graph of $f^\prime\left(x\right)$ , the slopes of $f\left(x\right)$ , and $f\left(x\right)$ will increase where its slopes are positive.
Approximate the interval over which $f$ is concave up. Justify your conclusion with the graph.
Hint (b):
Eyeball to see where you believe the point of inflections are in order to approximate the intervals. Note: Concave up is a U shape.
Is $f^{\prime\prime}\left(0\right)$ positive or negative? Explain how you know.
Hint (c):
$f^{\prime\prime}\left(x\right)$ represents the slopes of the given graph, $f ^\prime\left(x\right)$ . So look at the graph. Does it have a positive or a negative slope at $x = 0$ ?

Continuous curve, starting in upper left, concave up, turning at the approximate points, (negative 2.5, comma negative 7), & (4, comma 5.5), passing through the x axis at negative 5, 1, & negative 6, changing concavity at (1, comma 0).