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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

If |f^ (x) | 1 x R and f(0)=0=f^ (0) then which of the following can be TRUE?

Options

  1. Af ( 1 3 )= 1 5
  2. Bf (- 1 3 )= 1 4
  3. Cf(-3)= 1 3
  4. Dnone of these

Correct answer

C. f(-3)= 1 3

Step-by-step solution

According to LMVT aligned & | f^ (x)-f^ (0) x |= |f^ (C₁ ) | 1 & |f^ (x) | |x| & again by LMVT | f(x)-f(0) x |= |f^ (C₂ ) | |x| & f(x) x^2 aligned

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