In a phase diagram The critical point or critical state is the point at which two phases of a substance initially become indistinguishable from one another. For example to find the stationary points of one would take the derivative. When dealing with functions of a real variable a critical point is a point in the domain of the function where the function is either not differentiable or the derivative is equal to zero.
The function fleft x right x e x has a critical point local minimum at c 0.
And set this to equal zero. Again remember that while the derivative doesnt exist at w 3 w 3 and w 2 w 2 neither does the function and so these two points are not critical points for this function. Critical point mathematics in calculus the points of an equation where the derivative is zero Critical point set theory an elementary embedding of a transitive class into another transitive class which is the smallest ordinal which is not mapped to itself. In order to find critical points which are the points where the function might have extrema we just take the derivative of the original function set that derivative equal to 0 and then solve that equation for x.