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Let f : R ->(0,oo) and g : R -> R be ...

Let `f : R ->(0,oo)` and `g : R -> R` be twice differentiable functions such that f" and g" are continuous functions on R. suppose `f^(prime)(2)=g(2)=0,f^"(2)!=0` and `g'(2)!=0`, If `lim_(x->2) (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 atleast one `x in R`

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The correct Answer is:
A, D
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