Which one of the following statement is correct?

Options

AThe 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 if parallel to $y$ -axis
BThe 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
CThe 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
DNone of the above

Correct answer

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

Step-by-step solution

The correct answer is option C.

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