Answer :

x+y=8 y=8-x


Let f(x)=8x-x2

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


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


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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