Let f: R rarr R be a twice continuously ...

Let `f: R rarr R` be a twice continuously differentiable function such that f(0)= f(1)= f'(0)= 0. Then

f''(0)= 0

f''(c )= 0 for some `c in R`

if `c ne 0`, then `f''(c ) ne 0`

`f'(x) gt 0` for all `x ne 0`

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