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NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

If f x is a twice differentiable function such that f 0 = f 1 = f 2 = 0 , then

Options

  1. Af x = 0 has exactly 3 roots
  2. Bf ′ x = 0 for atleast 3 real values of x
  3. Cf ″ x = 0 for atleast 2 real values of x
  4. Df ″ x = 0 for atleast 1 real value of x

Correct answer

D. f ″ x = 0 for atleast 1 real value of x

Step-by-step solution

f x = 0 has atleast 3 real roots ∴ By Rolle’s theorem f ′ x = 0 has atleast two real roots and f '' x = 0 has atleast one real root.

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