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

Let f: `R to (0 ,oo)" and " g :R to R` be twice differentiable functions such that f and g are continuous functions on R. Suppose f(2) =g(2) =0, f(2) `ne` 0 and g(2) `ne` 0 if `lim_(x to 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 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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