Question

If Z = f(x, y) is a multivariable function then state the necessary and sufficient conditions

of Maxima and Minima.

Answer 1

If f(x,y)≤f(a,b) for all (x,y) in the domain of f, then f has a global maximum at (a,b). If f(x,y)≥f(a,b) for all (x,y) in the domain of f, then f has a global minimum at (a,b).

In other words, If there is a multivariable function and we want to find its maximum point, we have to take the partial derivative of the function with respect to both the variables. The partial derivatives will be 0.