1. Finding critical points

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

EX: $z=f(x,y)=2x^2+3y^2+xy-3y+3$

I need to find x, y, and z.

Thank you!

2. Originally Posted by eri123
How do you find the critical points of a function with more than one variable?

EX: $z=f(x,y)=2x^2+3y^2+xy-3y+3$

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 $V\left( -\frac3{23} , \frac{12}{23} , \frac{51}{23}\right)$ . This is the vertex of the eliptical paraboloid, drawn in red.