Which one of the following statements is correct?

Options

1. a.

   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

2. b.

   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

3. c.

   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

   Correct answer
4. d.

   None of the above