- #1
Addez123
- 199
- 21
- Homework Statement
- $$f(x,y,z) = xyz + xy$$
Boundaries are set by these 4 points:
(0,0,0), (1,0,0), (0,2,0), (0,0,2)
- Relevant Equations
- None
First step is to find the derivatives:
$$f_x' = yz + y$$
$$f_y' = xz + x$$
$$f_z' = xy $$
When all three equal zero, then you have a stationary point.
1. Let's start with f_z' = 0, when x = 0
Then $$y \in R$$
2. Knowing this we look at f_y' = 0
Since x = 0, z can be any real number just like y.
3. So we look at f_x' = 0
z = -1 and y can be any real number.
Our point of interest is then:
p = (0, y, -1)
This is my problem. That's a line, not a point.
Meaning any point on that line is a max,min?
Im confused..
$$f_x' = yz + y$$
$$f_y' = xz + x$$
$$f_z' = xy $$
When all three equal zero, then you have a stationary point.
1. Let's start with f_z' = 0, when x = 0
Then $$y \in R$$
2. Knowing this we look at f_y' = 0
Since x = 0, z can be any real number just like y.
3. So we look at f_x' = 0
z = -1 and y can be any real number.
Our point of interest is then:
p = (0, y, -1)
This is my problem. That's a line, not a point.
Meaning any point on that line is a max,min?
Im confused..