Question:
Let $\mathrm{S}$ be the set of all functions $f:[0,1] \rightarrow R$, which are continuous on $[0,1]$ and differentiable on $(0,1)$. Then for every $f$ in $S$, there exists a $c \in(0,1)$, depending on $f$, such that:
Correct Option: , 4
Solution:
For a constant function $f(x)$, option (1), (3) doesn't hold and by LMVT theorem, option (2) is incorrect.
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