Let f: r> (0, oo) and g: r rbe 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

Let f: R> (0, oo) and g: R Rbe 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 lim,-2 7E)S) Se)g{a) 1, then (1) f has a local minimum at r = 2 (2) f has a local maximum at z = 2 (3) f"(2) >> f(2) 4) f(r) -f"(r) = 0 for at least one z E R

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