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Let f be two differentiable function sat...

Let f be two differentiable function satisfying `f(1)=1,f(2)=4, f(3)=9`, then

A

f''(x)=2 for all `x in R

B

` f'(x)5= f''(x,) for some ` x in[1,3]`

C

there exists at least one` x in (1,3)` such that f''(x)=2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let `g(x) f=(x)-x^(2)`. Then,
g(x) has at least real roots in [1,3]
`rArr g'(x)` has at least 2 real roots in [1,3]
`rArr g''(x)` has at least one real root in [1,3]
`rArr f''(x)=2` for at least one `x in(1,3)`
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