MHT CET20239 May 2023Morning ShiftMathematicsApplication of DerivativesActual

The maximum value of x y when x+2 y=8 is

Options

Correct answer

D. 8

Step-by-step solution

aligned & x+2 y=8 & 2 y=8-x & y= 8-x 2 aligned Let f (x)=x y f (x)=x (8-x) 2 Differentiating w.r.t x , we get aligned f ^ (x) & = (8-x)-x 2 f ^ (x) & =4-x aligned To find critical points, array ll & f ^ (x)=0 & 4-x=0 & x=4 array critical point at x=4 f (4)= 4(8-4) 2 =8 Maximum value of the given function is 8 .

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