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Let f:RR to(0,oo)" and "g:RR to RR be tw...

Let `f:RR to(0,oo)" and "g:RR to RR` be twice differentiable functions such that f'' and g'' are continuous functions on `RR`. Suppose `f'(2)=g(2)=0,f''(2)ne0` and `g'(2)ne0`. If `underset(x to2)lim(f(x)g(x))/(f'(x)g'(x))=1`. Then

A

f has a local minimum at x = 2

B

f has a local maximum at x = 2

C

`f''(2)gtf(2)`

D

`f(x)-f''(x)=0` for at least one `x in RR`

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