Aplicaciones de la derivada al trazado de curvas

19:30 Jan 31, 2010 

Slothm:

I think you are probably thinking in terms of scattered points. Certainly, if you join all of them you are very likely to end up with something that is NOT a function. But the meaning of "trazado de curvas" here is the one that it has in Calculus, that is: abstract curves with infinite points that define a function (as opposed to scattered points that may or may not define a function).

:)

19:14 Jan 31, 2010 

Not only do derivatives are actually used TO SKETCH curves, but curve sketching is one of the main applications of derivatives at early stages of Calculus learning.

Derivatives and its graphical use

If there is a curve (or graph), there is a function that corresponds to that curve, no matter how strange the curve might be.

The first derivative of a function is the mathematical expression of the SLOPE of its corresponding curve at each of its points. It tells us whether the curve goes up or down.

The second derivative of a function is the matematical expression of the concavity of the curve at each of its points. It tells us whether the curve is convex or concave.

In a basic Calculus course people learn how to recognize the shape of functions (i.e. what kind of curve correspond to it) by looking at the first and second derivatives of that function.

If I know that a certain function has a positive first derivative and a negative second derivative throughout its whole domain I know for sure that the curve is one that is concave and goes up all the time. Then I can actually DRAW or SKETCH the shape of the function. Then I can draw or sketch the curve.

18:33 Jan 31, 2010 

The use of derivatives implies that a function exists.
The differential operator cannot be applied to data being represented in a graph, sketch or drawing.
The differential operator can be applied if there existe a curve
defined by Y=f(x). This curve implies a regression procedure.

03:54 Jan 31, 2010 

Absolutely right, plus curve fitting (regression, least squares etc.) is unlikely to be found in the first year of a maths degree (at least it wasn't in mine), yet alone a degree in accounting and finance.

03:45 Jan 31, 2010 

Maybe i'm being subjective here but I think "curve fitting" is something different from "trazado de curvas". From what I understand "curve fitting" refers to techniques that FIT a data set to a sort of average function that is in turn used for prediction. I think "trazado" is much accurately rendered by "drawing" or "sketching".

Cheers