CPM Homework Help : CALC3RD Problem 9-52

The graph at right shows $y = f^{\prime\prime}(x)$ . Use it to answer the following questions.

Over what interval(s) is $f$ concave up?
Hint (a):
$f$ is concave up when $f ^{\prime\prime}$ is positive. Where is the given graph positive?

Estimate $f^{\prime\prime\prime}(5)$ .
Hint (b):
This is asking for the slope of the given graph at $x = 5$ .

At what $x$ -value(s) does $f$ have a point of inflection?
Hint (c):
This is where $f ^{\prime\prime}$ changes sign. Where does the given graph change from negative to positive and vice versa?

At what $x$ -value(s) does $f^\prime$ have a minimum value?
Hint (d):
$f^\prime$ has a minimum where its slope changes from negative to positive.
The slope of $f^\prime$ is $f ^{\prime\prime}$ . So where does $f ^{\prime\prime}$ change from negative to positive?

Continuous curve labeled, f double prime of x, coming from left just below x axis, turning at the following approximate points, (0, comma 0), (1.5, comma negative 0.25), (3, comma 0.5), (5, comma negative 1), continuing up & right, passing through the x axis at 2, 4, & 6.