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Let f:Rrarr(0,oo)andg:RrarrR be twice di...

Let `f:Rrarr(0,oo)andg:RrarrR` be twice differentiable functions such that f'' and g'' are continuos functions of R suppose `f'(2)=g(2)=0,f'(2)ne0andg'(2)ne0.` If `underset(xrarr2)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 maximumatx=2

C

`f''(2) gt f(2)`

D

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

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The correct Answer is:
A, D
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