Contour diagram and second order of partial derivative

[-EquinoX-]

Homework Statement

The following contour diagram represents the function z = f(x,y)

http://img15.imageshack.us/img15/9059/contour.th.jpg

(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?

Homework Equations

The Attempt at a Solution

 

[Dick]

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]

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]

I already realized I'd been dozing. See the answer above. Sorry again.