The function \(f\left( x \right) = \frac{{tanx}}{x}\) at x = 0 has

Concept:

Maxima: A function f(x) is said to have a Maximum at x = c if there exist δ > 0 such that |x-c| < δ ; f(x) ≤ f(c).

Minima: A function f(x) is said to have a Minimum at x = c if there exist δ > 0 such that |x-c| < δ ; f(x) ≥ f(c).

Point of Inflection: The point at which a curve crosses its tangent is called the point of inflection. The function is neither maximum nor minimum at the point of inflection.

Calculation: 

Given,

The function is \(f\left( x \right) = \frac{{tan~x}}{x}\)

Since the above function is not defined for x = 0 so it is discontinuous at this point. As a result of this, the function f(x) will not be differentiable at x = 0

So, the correct answer will be option 1