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If f(0)=f(1)=f(2)=0 and function f(x) is...

If `f(0)=f(1)=f(2)=0` and function f(x) is twice differentiable in (0, 2) and continuous in [0, 2], then which of the following is/are definitely true ?

A

(a) `f''(c)=0, AA c in (0,2)`

B

(b) `f'(c)=0, "for atleast two "c in (0, 2)`

C

(c) `f'(c)=0, "for exactly one "c in (-0,2)`

D

(d) `f''(c)=0,` for atleast one `c in (0,2)`

Text Solution

Verified by Experts

The correct Answer is:
B, D
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