Accumulated Change and Antiderivative Plotter

 How to Run the Mathlet The mathlet has three modes that are chosen from the drop down menu located under the right window: Demo examples, User defined function, User drawn function. The Demo Examples mode illustrates the accumulated rate of change when a graph of the rate of change is given. The right window shows a graph of the rate of change of a population of bacteria, r(t), measured in thousands of bacteria per day, in the time interval from 0 to 20. The time, t, is measured in days, the population of bacteria, P(t), in thousands of bacteria. The initial population, P(0), is given in a box located between the two windows. Given a graph of the rate of change and the initial population, you are encouraged to sketch in the right window a possible graph of the population P(t) over the same time interval from 0 to 20. (You can graph in the window by dragging the mouse with the right mouse button depressed.) The Erase Sketch button can be used to erase the hand-drawn graph in order to sketch a new graph. The actual graph of the population P(t) is displayed by dragging the blue button of the slider located below the right window. The button Next Example provides a different graph for the rate r(t). The User Defined Function mode allows you to enter a formula for a function f(x). A function f(x) is entered in the input box below the right window. The syntax for doing so is the same as that used by most graphing calculators. All of syntax rules, as well as a list of available functions, are displayed by mousing over the button marked SYNTAX. You can choose the x- and y-ranges in the left window, as well as the y-range in the right window. (The x-range is the same in both windows.) The initial value for F(x), F(a) = b, at a point (a,b) can be entered in the box located between the two windows. After entering the data, press the GRAPH button. The graph of f(x) will appear in the left window. Again, you are encouraged to sketch the antiderivative F(x) in the right window. The actual antiderivative F(x) will be displayed by dragging the slider with the mouse. The RESET button clears the board and resets the ranges. The User Drawn Function mode lets you draw a function f(x) in the left window rather than specify a formula for it. This function may be piecewise continuous. You can choose x- and y-ranges, as well as the initial value for the antiderivative, F(a) = b, similarly to the previous option. Then the ENTER button must be pressed to register the entries. As in the other options, you can attempt to sketch F(x) and then display a (possibly more accurate) picture of F(x) by dragging the slider. The ERASE button clears the board and resets the ranges. © Copyright 2004 Barbara Kaskosz