Question

given f(x,y) = 2x^3+xy^2+5x^2+y^2. find local max, min values and saddle points.
Please help

Answer 1

i guess ... use the formula directly ...

Answer 2

I know to find critical point I have to have fx and fy and solve for x, y. but mine is fx= 6x^2+y^2+10x and fy= 2xy+2y^2 and stuck there

Answer 3

what happens when critical point occur?

Answer 4

from fx =0 , 6x^2 +y^2+10x =0, how to solve for y ? to your question; the graph change from decreasing to increasing or inverse, or saddle

Answer 5

yep ... two equations and two unknowns ... it's solvable.

Answer 6

as i posted, y^2= -6x^2 -10x. I can solve it? a negative number of the square?

Answer 7

6x^2+y^2+10x = 0
2xy+2y^2 = 0

Answer 8

or complex number?