In calculus, critical points or stationary points are any values of differentiable functions of complex or real variables whose derivative is 0, f(x0) = 0. In a differentiable function that has several real variables, critical points are values in the domain where the partial derivatives are 0. The values of critical points are known as critical values.
Critical points are important in calculus because they are used to find the minimum and maximum values of a graph. In the equation f(x0) = 0, "f" represents a function, and "x" represents the number or point that should be found. Setting the derivative of the function to be equal to zero, and solving for "x" ensures that one gets the critical number. Critical numbers can show up in values where the derivatives are not present. If a critical number can be taken back to its original function, the values of "x" and "y" that will be obtained will be the critical points. In some cases, critical points of function "f" can be defined as the values of "x" for which the graph has critical points for projection parallel to the different axis. These points are important when studying plane curves that are defined by implicit equations.