WBJEE · Maths · Application of Derivatives
Let \(f: R \rightarrow R\) be a twice continuously differentiable function such that \(f(0)=f(1)=f^{\prime}(0)=0 .\) Then
- A \(f^{\prime \prime}(0)=0\)
- B \(f^{\prime \prime}=0\) for some \(C \in A\)
- C if c \(\neq 0,\) then \(f^{\prime \prime}\neq 0\)
- D \(f^{\prime}(x)>0\) for all \(x \neq 0\)
Answer & Solution
Correct Answer
(B) \(f^{\prime \prime}=0\) for some \(C \in A\)
Step-by-step Solution
Detailed explanation
We have. \[f: \mathbb{R} \rightarrow \mathbb{R} \] be a twice continuousty differentiable function such that \(f(0)=f(1)=f'(0)=0\) Now, for atleast one value of \(\epsilon_{1} \in(0,1)\) \(f'\left(c_{1}\right)=0 \quad\) (by Rolle's theorem) Again. \(\quad f'(0)=0=f(c_{1})\)…
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