Concavity From A Second Derivative Table

Question

The table below provides selected values for $$f''(x)$$, the second derivative of the function $$f(x)=x^{3}-6x^{2}+9x+2$$. Based on the information in the table, on which interval is the graph of $$f$$ concave down?

|   x   | $$f''(x)=6x-12$$ |
|-------|------------------|
|   0   |       -12        |
|   2   |        0         |
|   4   |        12        |

Accepted Answer

For values of $$x < 2$$, since $$f''(x)=6*x-12$$ is negative, the function is concave down on $$(-\infty,2)$$.

Answer

The function is concave down only at $$x=2$$ where $$f''(x)=0$$.

Answer

For values of $$x > 2$$, the function is concave down because $$f''(x)$$ is positive.

Answer

The table does not provide any information about concavity.

x	$f''(x)=6x-12$
0	-12
2	0
4	12

Concavity From A Second Derivative Table

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