Absolute Extrema on a Closed Interval
What are the absolute minimum and absolute maximum values of the function $$f(x)=x^3-6x^2+9x+2$$ on the closed interval $$[2,5]$$? The table below shows the values of $$f$$ at the candidates for the absolute extrema.
| x | f(x) |
|---|---|
| 2 | 4 |
| 3 | 2 |
| 5 | 22 |
A
Absolute minimum: $$2$$ at $$x=3$$; Absolute maximum: $$22$$ at $$x=5$$.
B
Absolute minimum: $$2$$ at $$x=3$$; Absolute maximum: $$22$$ at $$x=3$$.
C
Absolute minimum: $$22$$ at $$x=5$$; Absolute maximum: $$2$$ at $$x=3$$.
D
Absolute minimum: $$4$$ at $$x=2$$; Absolute maximum: $$22$$ at $$x=5$$.
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