- #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..