f' (c) = 0 or f' (c) doesn't exist.
In geometric representation of the critical point can be means that the Tangent line is either horizontal, vertical or does not exist at that critical point on the curve.
A critical point of a function having two variables is a point where the partial derivative of First Order Differential Equation is equals to zero.
As we know that critical point is defined for the function where the gradient of the function is zero or undefined besides that every point at which a function takes a local maxima value is a critical point.
In the case of the single variable the partial Derivatives vanish at every critical point then the classification depends on the values of the second partial derivatives of the function.
To determine the critical points of a function we have to Set both partial derivatives of the function ‘f’ to zero and solve that for ‘x’ and ‘y’ separately. The values of the local minima or maxima are defined on the critical point. These concepts may be understood through the graph of the function f (x), a critical point on the graph does not Mean that tangent or tangents is a vertical or horizontal line.
For example the function g (t) = t2 + 2t + 3 is differentiable everywhere with the derivative 2t + 2. This function has a critical point -1 and this point is named as global minimum of the function g (t).