Chapter 5 - Slope

5.5 Geometrical Interpretation

The slope of an arbitrary function f(x) at x is interpreted as the slope of a straight line tengential to f(x) at x. This interpretation of the slope comes ultimately from the mathematical definition of the derivative as a limit Dx -> 0 of the Forward Difference formula.

Maple provides a powerful environment to illustrate this interpretation of the slope. In the following, the equation for the tangential straight line

y(x) = m x + b

is defined and plotted at various location along f(x). This allow to check "by eyes" the validity of the slope interpretation.

The steps are:

- calculate exactly the slope of f(x) - the Skewed Mexican Hat function.

- set the slope m = slope of f(x) at x = X (arbitrary position); therefore m = m(X)

- solve for b such that y(X) = f(X); therefore b = b(X)

- plot some of the tangential lines for various values of X

- plot these lines together with f(x) to illustrate that the lines are really tangential to f(x) for any X

Here is the actual Worksheet.


 
Section 5.4 Chapter 5 Section 5.6       TOC

Any questions or suggestions should be directed to
Michel Vallières at vallieres@physics.drexel.edu