Critical points of multivariables are points at which the gradient of a multivariable function is equal to zero. In other words, they are points where all partial derivatives of the function are equal to zero.
To find critical points of multivariables, you must first take the partial derivatives of the function with respect to each variable. Then, set each partial derivative equal to zero and solve the resulting system of equations to find the values of the variables at the critical point.
Critical points are important because they can help determine the maximum, minimum, or saddle points of a multivariable function. They are also used to find points of inflection and to optimize functions.
Yes, a multivariable function can have multiple critical points. In fact, most multivariable functions have more than one critical point.
Critical points are related to the graph of a multivariable function in that they correspond to points where the graph may have a local maximum, local minimum, or saddle point. They can also help determine the behavior of the function near those points.