Gradient of functions with multiple variables

[Niles]

Homework Statement

The gradient of f(x,y) = x^2-x+y is:

gradient_f(x,y) = (2x-1 ; 1). To find gradient_f(x,y), I set 2x-1 = 0 and 1 = 0 - so there are no points, where gradient_f(x,y) is zero because of 1 != 0?

 

[Niles]

And how to I find the maximum and minimum of the function, when there are no stationary points? (gradient_f(x,y) != 0)

 

[Kreizhn]

It's been awhile since I did Calc 3, but if you're in a bounded domain, you can apply the Extreme Value Theorem. Under those circumstances, the max/min likely lie on the boundary.