# Definition of the Derivative of a Function

The definition of the derivative in calculus, as the limit of the difference quotient, is explored interactively using an applet.

The function to be explored has the form **f(x) = a sin (b x + c) + d **where **a**, **b**, **c** and **d** are parameters that can be changed. A secant through two points **P** and **Q** (on the graph of function **f**) is made to approach what is called the tangent line, at point P
, to the graph of **f**.
__TUTORIAL__
1 - click on the button above "click here to start" and MAXIMIZE the window obtained.
2 - We start with two points $P$ and $Q$ on the graph of function f(x)= sin(x) (a = 1, b = 1, c = 0 and d = 0). Click on the button to make h (the difference in the x-coordinates of P and Q) smaller and notice how the secant through P and Q approaches what we call a tangent line to the graph of f. An important behavior to observe is also the convergence of the slope of the secant PQ to a finite value and that is the slope of the tangent line at x_{0}.
3 - Use the slider to change the coordinate of P and repeat the above experiment. Each time note the geometrical behavior of the secant and the convergence of its slope to a finite value which is called the derivative at that point.
4 - Use the sliders to change a, b, c and d. Each time note the geometrical behavior of the secant and the convergence of its slope to a finite value which is called the derivative at that point.
More references on derivatives and differentiation.
| |

Home Page --
HTML5 Math Applets for Mobile Learning --
Math Formulas for Mobile Learning --
Algebra Questions -- Math Worksheets
--
Free Compass Math tests Practice

Free Practice for SAT, ACT Math tests
--
GRE practice
--
GMAT practice
Precalculus Tutorials --
Precalculus Questions and Problems
--
Precalculus Applets --
Equations, Systems and Inequalities
--
Online Calculators --
Graphing --
Trigonometry --
Trigonometry Worsheets
--
Geometry Tutorials --
Geometry Calculators --
Geometry Worksheets
--
Calculus Tutorials --
Calculus Questions --
Calculus Worksheets
--
Applied Math --
Antennas --
Math Software --
Elementary Statistics
High School Math --
Middle School Math --
Primary Math

Math Videos From Analyzemath

Author -
e-mail

Updated: 2 April 2013
Copyright © 2003 - 2014 - All rights reserved