Let f: R (0, ) and g: R R be twice differentiable functions such that f'' and g'' are continuous functions on R . Suppose f'(2)=g(2)=0, f''(2) 0 and g'(2) 0. If _ x 2 f(x)g(x) f'(x)g'(x) =1, then

JEE Advanced 2016 Mathematics question

Let and be twice differentiable functions such that and are continuous functions on . Suppose , and . If , then

Answer: (A),(D)

At numerator and denominator both vanish (, ). L'Hospital's rule: , so

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Question ID VK-026582