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AP EAMCET2001MathematicsApplication of Derivatives

The maximum value of x y subject to x+y=7 is

Options

  1. A10
  2. B12
  3. C49 4
  4. D55 4

Correct answer

C. 49 4

Step-by-step solution

Let M=x y aligned M & =x(7-x)=7 x-x^2 [ x+y=7 given ] d M d x & =7-2 x aligned For maximum or minimum, put d M d x =0x= 7 2 d^3 M d x^2 =-2=-v e The maximum value at x= 7 2 = 7 2 (7- 7 2 )= 7 2 ( 7 2 )= 49 4

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