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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

f(x) is defined for x -1 and has a continuous derivate. If f satisfies f(0)=1, f^ (0)=0 ; (1+f(x)) f^ (x)=1+x . If x is positive then f^ (x) is

Options

  1. Aalways positive
  2. Balways negative
  3. Calways non-negative
  4. Dnone of these

Correct answer

A. always positive

Step-by-step solution

f^ (x)= 1+x 1+f(x) . Also f^ (x) 0 f^ (x) is increasing f^ (x) ^ (0)=0 x 0

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