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KVPY2010MathematicsApplication of Derivatives

Let f: R R be a differentiable function such that f(a)=0=f(b) and f^ ( . a) f^ (b)>0 for some a < b . Then the minimum number of roots of f^ (x=0 in the interval (a, b) is-

Options

  1. A3
  2. B2
  3. C1
  4. D0

Correct answer

B. 2

Step-by-step solution

f^ (a), f^ (b)>0 so either both are positive or both are negative f ( a )= f ( b )=0 2 roots

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