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Question

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the xaxis and vertices C and D lie on the parabola, y=x21 below the xaxis, is

A
433
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B
43
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C
233
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D
133
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Solution

The correct option is A 433

Area =2a(a21)
(Say) A=2a32a
dAda=6a22
For maximum and minimum, dAda=0
6a22=0
a=±13
Now, d2Ada2=12a
At a=13
d2Ada2=43>0
a=13 (rejected)

At a=13
d2Ada2=43<0
Maximum area
=(2a32a)=(233+23)
=433 sq. units

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