APFIVE Absolute Extrema On A Closed Interval
A company’s profit is modeled by the quadratic function $$f(x)= -x^2+4*x+5$$ over the interval $$[0,5]$$. Use the Extreme Value Theorem to determine the absolute maximum and minimum values of the profit on this interval.
| x | f(x)= -x^2+4*x+5 |
|---|---|
| 0 | 5 |
| 2 | 9 |
| 5 | 0 |
A
Absolute maximum: $$9$$ at $$x=2$$; Absolute minimum: $$0$$ at $$x=5$$.
B
Absolute maximum: $$9$$ at $$x=2$$; Absolute minimum: $$5$$ at $$x=0$$.
C
Absolute maximum: $$5$$ at $$x=0$$; Absolute minimum: $$0$$ at $$x=5$$.
D
Absolute maximum: $$0$$ at $$x=5$$; Absolute minimum: $$9$$ at $$x=2$$.
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