# Contour diagram and second order of partial derivative

#### -EquinoX-

1. Homework Statement
The following contour diagram represents the function z = f(x,y)

http://img15.imageshack.us/img15/9059/contour.th.jpg [Broken]

(a) Is z an increasing or decreasing function of x?
I'd say it's increasing as it goes towards the x-axis the contour lines value goes down
(b) Is z an increasing or decreasing function of y?
I'd say it's decreasing as it goes towards the y-axis the contour lines value goes down
(c) Is fxx positive or negative?
I think it's negative
(d) Is fyy positive or negative?
I think it's negative
(e) Is grad f longer at point P or Q?
Q

Is my answer correct?
2. Homework Equations

3. The Attempt at a Solution

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#### Dick

Science Advisor
Homework Helper
I'd agree with all of your answers. I'm I little confused about the reasoning on some of them. E.g. for a) I'd say it's an increasing function of x because z is increasing as you move away from the y-axis. Oh, I think I see what you mean. You mean f is increasing as you move ALONG the x-axis.

#### -EquinoX-

I just tried my answer and c) is supposed to be positive why is this?

#### Dick

Science Advisor
Homework Helper
Yeah, you're right. Sorry. As you move along the x-axis from a point z is increasing at an increasing rate since the contours are spaced closer together as you move in the positive x direction. I guess I wasn't paying close attention. Sorry again. Also think I might have been asleep at the wheel for e). The magnitude of grad is proportional to the maximum rate of change at a point, right? Closer contours mean faster rate of change.

#### -EquinoX-

and why is the answer to part e) P?

#### Dick

Science Advisor
Homework Helper
I already realized I'd been dozing. See the answer above. Sorry again.

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