were can i get details on physical and geometrical interpretation of derivativess?

Answer 1

Travis is just a little off. Derivatives are used in everyday life, whether it's engineering, statistics, or someone just trying to make an educated guess on income in a small business. Derivative is a word meaning, rate of change, or a word that informs where something came from.
In the geometrical interpretation, it is used in polynomials to describe the rate of change. when using values in place of variables, it describes the rate of change at a given point. But, putting it in the most basic sense, a square is a derivative of a pentagon. While a triangle is a derivative of a square. Do you see the relationship? And then in the physical sense, you are a derivative of your parents.

Answer 2

Hmm I think what you are asking is what exactly a derivitive is when you are talking about the physical world???

Well, first what a derivitive is is just a formla for finding the slope of a line (in 2 dimensions) at anywhere on that line. There is nothing really phyisical about it. I would call it a mathematical tool that would tell you somthing about an equation or shape. Really what you are doing is using one math equation to describe another.

let's look at a simple graph of a function: F(x)= x^2 + 2x +2

regardless of how that looks when graphed one question we can ask is well what is the slope of this graph at some point on the line. Well we can accually go one step farther and ask "What is the slope of this graph on ANY point of the graph?"

that's what we use a derivitive for ... ok so let's do that

f'(x)= 2x +2 .. now we can plug any point that is in this graph in for x and find it's slope at that point... Really what we are finding is the slope of the tangent line to this graph, but it is the same thing.

In three dimensions it is pretty much the same deal but here we must do partial derivitives so that we can say we are looking for a general slope of a field... same deal just a bit more complicated. hope that helps