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Manipal MET2021MathematicsApplication of Derivatives

The function x(1+ x), 0 x 2 has maximum value, when x is equal to

Options

  1. A0
  2. B2
  3. C6
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

aligned & ( Let z= x(1+ x) & or z= x+ 1 2 2 x aligned On differentiating w.r.t. x , we get d z d x = x+ 2 x For maximum or minimum, put d z d x =0 array rlrl & x+ 2 x & =0 & 2 ^2 x-1+ x & =0 & ( x+1)(2 x-1) & =0 & & x & =-1, 1 2 & & x & = 3 , array But 0 x 2 , therefore we take only x= 3 . d^2 z d x^2 =- x-2 2 x=- ve, for x= / 3 It is maximum at x= / 3 .

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