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Let f(x) be a nonzero function whose al...

Let `f(x)` be a nonzero function whose all successive derivative exist and are nonzero. If `f(x), f' (x) and f''(x)` are in G.P. and `f (0) = 1, f '(0) = 1`, then -

A

`f(x) gt 0 forall X in R`

B

`f'(x) gt 0 forall X in R`

C

`f'''(0) = 1`

D

`f(x) le 1 forall X in R`

Text Solution

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The correct Answer is:
A, B, C
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