Absolute Extrema on a Closed Interval

Question

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   |

Accepted Answer

Absolute minimum: $$2$$ at $$x=3$$; Absolute maximum: $$22$$ at $$x=5$$.

Answer

Absolute minimum: $$2$$ at $$x=3$$; Absolute maximum: $$22$$ at $$x=3$$.

Answer

Absolute minimum: $$22$$ at $$x=5$$; Absolute maximum: $$2$$ at $$x=3$$.

Answer

Absolute minimum: $$4$$ at $$x=2$$; Absolute maximum: $$22$$ at $$x=5$$.

Absolute Extrema on a Closed Interval

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