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Finding extreme values for functions of two variables

1.)f(x,y)= 2x^2 + xy^2 + 5x^2 + y^2

2.)f(x,y)= ysquareroot x - y^2 - x + 6y

Solution Summary

Finding the local extreme values of functions of a single variable entails investigating the stationary points where the derivative is zero. The existence and value of global extremes additionally requires investigation of what occurs toward the edges of the domain of definition. This approach can be generalised to functions of two variables, where finding stationary points involves simultaneously solving for stationary points of the partial derivatives and then applying a more generalised "second derivative" test to describe their character. The solution consists of two pages written in Word with equations in Mathtype illustrating the application of these ideas. Each step is explained.