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Poetria

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- Homework Statement
- h(x,y)=x*y

x,y, h are measured in meters

A guy starts walking at the point (2,1) and continues in a straight line to (0,3).

As he starts, he is walking uphills if I understand it correctly.

The slope at the moment he starts is required.

Then a unit vector which is tangent to the level curve of h at height 2 at the point (2,1).

Finally - directional derivative ##D_\vec u h(2,1)##

- Relevant Equations
- $$y'=-\frac {F_x} {F_y}$$

$$h_x=y$$

$$h_y=x$$

Substituting the coordinates of a given point:

$$y'=-\frac {y} {x}$$

$$y'=-\frac {1} {2}$$

A unit vector:

$$\frac {1} {\sqrt{5}, \frac {2} {\sqrt{5}}$$

$$D_\vec u h(2,1) = \frac {1} {\sqrt{5}, \frac {2} {\sqrt{5}} \cdot \vec (1,2)$$

$$D_\vec u h(2,1) = \frac {5} {\sqrt{5}}$$

$$h_y=x$$

Substituting the coordinates of a given point:

$$y'=-\frac {y} {x}$$

$$y'=-\frac {1} {2}$$

A unit vector:

$$\frac {1} {\sqrt{5}, \frac {2} {\sqrt{5}}$$

$$D_\vec u h(2,1) = \frac {1} {\sqrt{5}, \frac {2} {\sqrt{5}} \cdot \vec (1,2)$$

$$D_\vec u h(2,1) = \frac {5} {\sqrt{5}}$$

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