Differentiation 1

The applets are started by clicking the red buttons.

 On the definition of the derivative is a dynamical diagram displaying the derivative as the slope of the tangent to a graph. In this way, the most important notions for the discussion of graphs can be learned even before the formal manipulations of differental calculus are known. The necessary preliminaries the user should be familiar with are the slope of a straight line and the graph of a function (see the two applets The slope of a straight line und Function and graph). The applet is started from the red button in its own window.

 The Derivative puzzles are three applets of puzzle game type: the goal is to place given graphs such that below each graph the graph of its derivative located. On demand a text informing about the success achieved so far (and - if necessary - stating why some of the choices are wrong) is displayed. The applets shall strengthen the understanding of differentiation as a process leading from one function to another. The first applet is quite easy to solve, since it involves only polynomial functions. Number 2 and 3 are a bit more difficult. The applets are started from the red buttons in their own windows.
 Also visit the   big derivative puzzle of the interactive tests section, which chooses out of more than 50 functions by random and evaluates the success achieved.

 The applet First and second derivative helps to understand the concept of the second derivative (the rate of change of the rate of change) of a function. It shows graphs of functions of the type f(x) = a + b x + c x2 + d x3, together with their first two derivatives. The parameters a, b, c und d may be ajusted by means of scrollbars. Thus, relations between properties of functions (with respect to zeros, extrema, i.e. minima and maxima, and inflection points) may be discussed at a geometrical level. The applet is started from the red button in its own window.