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MHT CET20227 Aug 2022Evening ShiftMathematicsApplication of DerivativesActual

Two positive numbers x and y such that (x+y)=60 and x y^3 is maximum, then the numbers are respectively

Options

  1. A45,15
  2. B30,30
  3. C20,40
  4. D40,20

Correct answer

A. 45,15

Step-by-step solution

x+y=60 x=60-y Now let z=x y^3=(60-y) y^3=60 y^3-y^4 d z d y =180 y^2-4 y^3=4 y^2(45-y) i.e., x y^3 is maximum y=45 and x=60-45=15

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