Which of the following statement is correct?

Options

A. The derivative of a function f(x) at a point will exist if there is one tangent to the curve y = al the point and the tangent is parallel to y-axis.
B. The derivative of a function f(x) at a point will exist if there is one tangent to te curve y = f(x) at the point and Ihe tangent must be parallel to y-axis
C. The derivative of a function f(x) at a point will exist if there is one and only one tangent lo the curve `y =f(x)` at the point and the tangent is not parallel to y-axis.
D. none of these

Answer

C