Intervals of Increase and Decrease

Question

Consider the following statements regarding the function $$f(x)=x^3-6x^2+9x+2$$.

I. The derivative of $$f$$ is $$f'(x)=3x^2-12x+9$$, and its critical numbers are $$x=1$$ and $$x=3$$.

II. The function $$f$$ is decreasing on the interval $$(-\infty, 1)$$.

III. The function $$f$$ is increasing on the interval $$(3, \infty)$$.

The table below shows selected values for the function $$f$$.

| x | f(x) |
|---|---|
| 0 | 2 |
| 1 | 6 |
| 2 | 4 |
| 3 | 2 |
| 4 | 6 |

Which of the statements above is/are true?

Accepted Answer

Statements I and III only are true.

Answer

All statements are true.

Answer

Only statement I is true.

Answer

Statements II and III are true.

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