[Agent-X]

I'm trying to figure out how to do instantaneous rates, but it seems like I need to know calculus to do this. I don't know calculus, and it wasn't listed as a prerequisite; I wasn't told the first day I need to know anything beyond basic algebra.

Anyway, I'm suppose to find the "slope of a line tangent to the curve at any point."

I don't really understand that. I tried searching for hours about this stuff, and I couldn't really find anything to help me; well, I tried analyzing stuff, but I couldn't see how it applied to what I was doing.

The book didn't have that information.

I know how to find the slope of something. But drawing this line against the curve... I don't know how to do that.

Therefore, I decided to come here.

Attached to this post is an image.
It's giving an example of instantaneous rate.

Thing is, I don't exactly understand how the authors were able to get that line next to the point (t=600) on the graph.

No equation has been giving to figure out how to do that.

The book also tells me this:

http://img357.imageshack.us/img357/6097/equationpe8.jpg

I'm not very sure about how it obtained those top variables. It seems like it picked them out of thin air. If I'm correct, though, those variables come from the points that the slope comes across. However, I couldn't know those points unless I had done all of this in a graphing calculator, right?

I haven't the slightest clue how those top variables were obtained, nor do I have the slightest clue how to make that line go against the point of the curve.

How do I do these things?

[Borek]

http://en.wikipedia.org/wiki/Tangent

See first (geometrical) meaning of tangent.

When you have a plot you can almost always draw tangent line just looking at the curve. When you have tangent line you can use it as hypotenuse to "build" a right triangle (with legs parelel to plot axes). That's what they did, thats where both delta values come from.