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Question

Let f(x,y)=xy2 if x and y satisfy x2+y2=9 then the minimum value of f(x,y) is

A
0
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B
33
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C
63
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D
36
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Solution

The correct option is D 63
We have,
f(x,y)=xy2,x2+y2=9y2=9x2(ii)Then,f(x,y)=x(9x2)f(x,y)=(9xx3)

f(x,y)=93x2=093x2=03(3x2)=0x2=3x±3andy2=93=6

Then, maximum value of f(x,y)=3×6=63.

Hence, this is the answer.

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