99 Percentile Qs Bank for JEE MainMathematicsApplication of Derivatives

The maximum area of the rectangle that can be inscribed in a circle of radius r , is

Options

Ar²
Br²
Cr² / 4
D2 r²

Correct answer

D. 2 r²

Step-by-step solution

Area of rectangle, aligned A &=2 x 2 r²-x² &=4 x r²-x² d A d x &= 4 (r²-2 x² ) r²-x² aligned For maximum or minimum put d A d x =0 x=r / 2 It can be easily checked that d² A d x² < 0 for this value of x . A is maximum for x= r 2 and the maximum value of A is given by A=4 r 2 r²- r² 2 =2 r²

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