APFIVE Intervals of Increase and Decrease
I. For the function $$f(x)=x^3-6*x^2+9*x+2$$, the derivative is $$f'(x)=3*x^2-12*x+9$$ with critical numbers at $$x=1$$ and $$x=3$$.
II. The function f is decreasing on the interval $$(-\infty,1)$$.
III. The function f is increasing on the interval $$(3,\infty)$$.
Based on the derivative and the table of values provided, which statements are true about the behavior of f?
| x | f(x) |
|---|---|
| 0 | 2 |
| 1 | 6 |
| 2 | 4 |
| 3 | 2 |
| 4 | 6 |
A
Statements II and III are true.
B
Statements I and III only are true.
C
All statements are true.
D
Only statement I is true.
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