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AP EAMCET2003MathematicsApplication of Derivatives

The sum of two numbers is 20 . If the product of the square of one number and cube of the other is maximum, then the numbers are :

Options

  1. A12,8
  2. B3,4
  3. C9,12
  4. D15,18

Correct answer

A. 12,8

Step-by-step solution

Let the numbers be x, y . x+y=20 y=20-x Let S=x^3(20-x)^2 On differentiating w.r.t x , we get d S d x =2 x^3(20-x)(-1)+3 x^2(20-x)^2 For maximum or minimum, put d S d x =0 x^2(20-x)(-2 x+60-3 x)=0 x=0, x=12 or x=20x cannot be 0 or 20 When x=12 , then y=20-12=8 The required numbers are 12,8 .

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