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MHT CET2011MathematicsApplication of Derivatives

For all real x , the minimum value of 1-x+x² 1+x+x² is

Options

  1. A0
  2. B1 / 3
  3. C1
  4. D3

Correct answer

B. 1 / 3

Step-by-step solution

Let y= 1-x+x² 1+x+x² =1- 2 x 1+x+x² aligned &=1- 2 1 x +1+x y &=1- 2 t aligned where t= 1 x +1+x Now, y is minimum, when 2 t is t is min . array lc & d t d x =- 1 x² +1=0 x= 1 d² t d x² = 2 x³ >0, for x=1 array Minimum value of y is aligned 1- 2 1+1+1 &=1- 2 3 &= 1 3 aligned

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