If I have a multivariable equation whose slope is always positive, say how do I demonstrate that the slope is always positive?

I imagine this involves partial derivatives but need some guidance.

Thanks

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- February 21st 2010, 09:37 AMrainerNeed to demonstrate that the slope is strictly positive
If I have a multivariable equation whose slope is always positive, say how do I demonstrate that the slope is always positive?

I imagine this involves partial derivatives but need some guidance.

Thanks - February 21st 2010, 12:10 PMtonio
- February 22nd 2010, 10:41 AMrainer
Oh yeah, good point.

Let me give a few more parameters.

First, I reduce the equation to 3 variables:

So it's a 3D graph. I am interested in the slope on the 2D x-y plane or "cross-section" of the origin.

Does that narrow it down enough? - February 22nd 2010, 02:12 PMmaddas
I don't understand your definition. The definiton I am familiar with says a function has positive slope iff for every injective curve whose coordinate functions are increasing, the derivative of is positive. Is this what you want?

- February 24th 2010, 07:57 AMrainer

Hmmm, this definition is really cool-looking. But not understanding the half of it I will have to say I don't know if it's what I need or not.

It looks like I need to ruminate and clarify whatever it is I am trying to ask. So let's leave off here and maybe I'll post a clarified version of my question in a new thread.

Thanks a lot - February 24th 2010, 10:05 AMHallsofIvy
The difficulty appears to be that

**you**do not know what**you**mean by "slope" of a multivariable function. In order to be able to talk about slope being positive, you must mean it to be a number, but**what**number?