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For all twice differentiable functions \(f: R \rightarrow R\), with \(f(0)\) \(=f(1)=f^{\prime}(0)=0 \) [JEE Main 2020, …

Q1

For all twice differentiable functions \(f: R \rightarrow R\), with \(f(0)\) \(=f(1)=f^{\prime}(0)=0 \)

[JEE Main 2020, 6 Sep (Shift 2)]

a

\(
f^{\prime \prime}(0)=0
\)

b

\(
f^{\prime \prime}(x)=0, \text { for some } x \in(0,1)
\)

c

\(
f^{\prime \prime}(x)=0 \text {, at every point } x \in(0,1)
\)

d

\(
f^{\prime \prime}(x) \neq 0 \text {, at every point } x \in(0,1)
\)

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