- #1
knowLittle
- 312
- 3
Homework Statement
f(x,y)= 16(y^2) +(x^4) y + 4(x^2) + 4
My problem is recognizing which critical points to consider valuables.
Homework Equations
fxx, fyy, fxy, and second partials test.
D=fxx(fyy)- (fxy)^2
The Attempt at a Solution
I found:
fx=0
4(x^3)y +8x=0
(x^2) y= -2
Now, from here I can discern that either
x=+-1 , y= -2 **this solution is not considered in the solutions manual. Anyone care to explain**
OR
x=2, y= -(1/2) OR
x= -2, y= -1/2
Also, I was thinking about plugging in values of the other fy=0 part. It gets even more complicated.
Now:
fy=0
32y + (x^4) =0
y= -(x^4)/32
From here the only thing I thought about was
x=0, y=0.
I also thought about solving for y and replacing on the other fx equation, but things don't look good and the solutions shows that it's wrong.
Can anyone give me tips to discern critical points?
Thank you.