Q16 of 137 Page 19

#Mark the correct alternative in each of the following

If x + y = 8, then the maximum value of xy is


x+y=8 ⇒ y=8-x

xy=x(8-x)


Let f(x)=8x-x2


Differentiating f(x) with respect to x, we get


f’(x)=8-2x


Differentiating f’(x) with respect to x, we get


f’’(x)=-2<0


For maxima at x=c, f’(c)=0 and f’’(c)<0


f’(x)=0 ⇒ x=4


Also f’’(4)=-2<0


Hence, x=4 is a point of maxima for f(x) and f(4)=16 is the maximum value of f(x).

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