Question

If lim as x approaches 3 at f(x)/(2x-6)=f'(3)=0 which of the following must be true? I) (3,0) is a critical point of f(x). II) f(x) has a local minimum at x=3 III) f(x) is continuous at x=3 a) I only b) II only c) III only d) I and III only e)I II and III

Answer 1

The answer is d. 

F'(3)=0 so there is a critical point at x=3.

We don't know if the point at x=3 is a min or max since the original function is not given

In order for a function to be differentiable at a point it must also be continuous by definition.