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CUET
-- Applied Mathematics - Section B2
Calculus
For $x+y = 8 ,$ the maximum value of xy is :
4
8
32
16
The correct answer is Option (4) → 16
$x+y=8$
$⇒y=8-x$
Now,
$xy=x(8-x)=8x-x^2$
and,
$\frac{d}{dx}(8x-x^2)=8-2x$
$⇒8-2x=0$
$⇒x=4,y=4$
$⇒xy=16$
