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Let f(x) be a twice differentiable funct...

Let `f(x)` be a twice differentiable function for all real values of `x` and satisfies `f(1)=1,f(2)=4,f(3)=9.` Then which of the following is definitely true? (a) `f^('')=2AAx in (1,3)` (b) `f^('')=f(x)=5forsom ex in (2,3)` (c) `f^('')=3AAx in (2,3)` (d) `f^('')=2forsom ex in (1,3)`

A

`f''(x)=2AAx in(1,3)`

B

`f''(x)=f(x)5"for some"x in(2,3)`

C

`f''(x)=3AAx in(2,3)`

D

`f''(x)=2"for some"x in(1,3)`

Text Solution

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The correct Answer is:
D
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