Thread: Finding critical points

How do you find the critical points of a function with more than one variable?

EX:

I need to find x, y, and z.

Thank you!

Originally Posted by eri123

How do you find the critical points of a function with more than one variable?

EX:

I need to find x, y, and z.

Thank you!

1. Differentiate f(x,y) wrt x and afterwards differentiate f(x,y) wrt y. Both derivations must equal zero.

2. Solve the system of equations for x and y. Plug in the results into the equation of the function. I've got . This is the vertex of the eliptical paraboloid, drawn in red.