Which one of the following statements is correct?

The derivative of a function f(x) at a point will exist if there is one tangent to the curve y = f(x) at that point and the tangent is parallel to y-axis

The derivative of a function f(x) at a point will exist if there is one tangent to the curve y = f(x) at that point and the tangent must be parallel to x-axis

The derivative of a function f(x) at a point will exist if there is one and only one tangent to the curve y = f(x) at that point and the tangent is not parallel to y-axis

None of the above