Faith E.

asked • 10/31/22

A rectangle is bounded by the x-axis and the semicircle y = sqrt (49 − x2) . What length and width should the rectangle have so that its area is a maximum?

Doug C.

Take a look at this graph to see if you can figure out how to set up the area function (depending on x), take the derivative and determine critical number(s), confirm that the critical number generates a max value, then find that max value for the target critical number. desmos.com/calculator/dqwz7jpzoa
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10/31/22

Doug C.

Once you have given it a try I have a graph that shows the answer.
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10/31/22

Doug C.

Hint: taking the derivative of the area function requires the use of the product rule (and chain rule).
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10/31/22

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Doug C. answered • 10/31/22

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