A rectangle is to be inscribed in a semicircle of radius 10 cm such that one side of…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A rectangle is to be inscribed in a semicircle of radius 10 cm such that one side of the rectangle lies along the diameter. (i) Find the dimensions of the rectangle that give the greatest possible area. (ii) Prove that this area is the maximum attainable within the semicircle.

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