APFIVE Concavity From A Second Derivative Table
Which of the following is an example of using table-based analysis to identify an interval where a function is concave down? Based on the table for the second derivative of $$f(x)=x^{3}-6*x^{2}+9*x+2$$, select the correct interval.
| x | f’'(x)=6*x-12 |
|---|---|
| 0 | -12 |
| 2 | 0 |
| 4 | 12 |
A
For values of $$x > 2$$, the function is concave down because $$f''(x)$$ is positive.
B
The table does not provide any information about concavity.
C
For values of $$x < 2$$, since $$f''(x)=6*x-12$$ is negative, the function is concave down on $$(-\infty,2)$$.
D
The function is concave down only at $$x=2$$ where $$f''(x)=0$$.
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