Question

There is one critical point for z = x^5y + xy^5 + xy. Find it.

Answer 1

can someone just explain how to get started??

Answer 2

take partial
dz/dx= 5x^4 y + y^5 +y
dz/dy= x^5 +x 5y^4+x

Answer 3

set partial=0

Answer 4

ok and that is the critical point? seemed more confusing in the text. thanks!

Answer 5

I got x=0 y=0

Answer 6

x=0 y=0 makes both partial zero

Answer 7

would the same method by applied here as well?? Find the critical point(s) of f(x, y) = 1 + (x − y)^2 + (x − 1)^2

Answer 8

Yes,

Answer 9

ok thank you!!

Answer 10

It is basically just like critical value in calc I but we have both x and y so it is called crictle points

Answer 11

oh ok!