Question

a contour diagram of z=f(x,y) is given in the figure. Determine whether fx and fy are positive, negative, or zero at the points P, Q, R, and S.

Answer 1

Is there a legend that shows what z values corresponds to which shade of color?

Answer 2

nope this is everything i am given in my question and a picture of it

Answer 3

You can think of a contour diagram as a topographical map. Each circle, or in this case shade, represents as elevation/ z-value.

Answer 4

maybe @ajprincess or @hartnn knows??

Answer 5

ohhh wait a minute.. fx is a partial derivative

Answer 6

Okay so lets look at \(f_{x}\) at R:
That is the change in x with respect z
If you draw a line from left to right that passes through r would the line fall down or rise up?

Answer 7

**near the area of r**

Answer 8

depends on where you start the line

Answer 9

what would be happening at r?

Answer 10

It would be going down.. At R as x changes in the positive direction z changes in the negative direction. Therefore \(f_{x}\) at R is negative.

Answer 11

Lets look at \(f_{x}\) at point P.

We are interested in \[\Delta x \over \Delta z\] at point P

Answer 12

As x changes in the positive direction:

Answer 13

The surface is going up hill

Answer 14

ok i understand thank you

Answer 15

no problem