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Black Book Advanced Problems in MathematicsMathematicsApplication of Derivatives

Let m and n be positive integers and x, y > 0 and x + y = k , where k is constant. Let f(x, y) = x^m y^n , then :

Options

  1. Af(x, y) is maximum when x = mk m+n
  2. Bf(x, y) is maximum where x = y
  3. Cmaximum value of f(x, y) is m^n n^m k^ m+n (m+n)^ m+n
  4. Dmaximum value of f(x, y) is k^ m+n m^m n^n (m+n)^ m+n

Correct answer

A. f(x, y) is maximum when x = mk m+n

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