Question

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Which one of the following statement is correct?

MathematicsApplication of DerivativesNDANDA 2012 (Phase 1)

Options:

A The derivative of a function $\mathrm{f}(\mathrm{x})$ at a point will exist if there is one tangent to the curve $\mathrm{y}=\mathrm{f}(\mathrm{x})$ at that point and the tangent is parallel to y-axis
B The derivative of a function $\mathrm{f}(\mathrm{x})$ at a point will exist if there is one tangent to the curve $\mathrm{y}=\mathrm{f}(\mathrm{x})$ at that point and the tangent must be parallel to $\mathrm{x}$ -axis
C The derivative of a function $\mathrm{f}(\mathrm{x})$ at a point will exist if there is one and only one tangent to the curve $\mathrm{y}=\mathrm{f}[\mathrm{x}]$ at that point and the tangent is not parallel to y-axis
D None of the above