Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola.
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nswer:
≈17.418 sq. units.
Explanation:
A(x)=2x(8−x2)=16x−2x3
A'(x)=16−6x2=0⇒x=±√83
There is a maximum at x=√83.
So the dimensions that will produce the greatest area are:
2×√83 for the base and 513 for the height.
The maximum area is: 2√83×163≈17.418

≈17.418 sq. units.
Explanation:
A(x)=2x(8−x2)=16x−2x3
A'(x)=16−6x2=0⇒x=±√83
There is a maximum at x=√83.
So the dimensions that will produce the greatest area are:
2×√83 for the base and 513 for the height.
The maximum area is: 2√83×163≈17.418

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