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JEE Main 20206 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Application of Derivatives

JEE Main 2020 · 6 September · Evening Shift · Mathematics · Application of Derivatives

For all twice differentiable functions f: R → R , with f(0) = f(1)...

For all twice differentiable functions f:R→Rf: R \to R, with f(0)=f(1)=f′(0)=0f\left(0\right) = f\left(1\right) = f ' \left(0\right) = 0,

Options

  1. Af " \left(x\right) \ne 0ateverypointat every pointxε\left(0, 1\right)
  2. Bf " \left(x\right) = 0,forsome, for somexε\left(0, 1\right)
  3. Cf"(0)=0f " \left(0\right) = 0
  4. Df " \left(x\right) = 0,ateverypoint, at every pointxε\left(0, 1\right)

Correct answer

D. f " \left(x\right) = 0,ateverypoint, at every pointxε\left(0, 1\right)

Step-by-step solution

Applying Rolle's theorem in [0,1] for function f(x)f ( x )

f′(c)=0,cε(0,1)f ' \left(c\right) = 0, cε\left(0, 1\right)

again applying Rolle's theorem in [0, c] for function f′(x)f ' ( x ),

f ' ' \left(x\right) = 0, c \in \left(0, 1\right)

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