Explore function derivatives with this applet. You can enter a function of [math]x[/math] in the entry box. Some functions to consider include[br][list][*]sin(x)+1[/*][*]log(x)[/*][*]tan(x)[/*][*]asin(x)[/*][*]cos(x)+1[/*][*]exp(x)[/*][*]x^2[/*][*]-x^2[/*][/list][br]The lower graph shows either the first or second derivative of the function. If "Show Negative Derivative" is selected a highlight will indicate where the derivative is negative on both plots.

Enter any function.[list=1][br][*]Show the first derivative. ( Uncheck 2nd Derivative )[list=1][*]Is the blue curve increasing or decreasing where the derivative is negative?[br][*]Do you notice anything about the function where the derivative crosses zero?[br][/list][br][*]Show the second derivative[list=1][*]What can you say about the blue function where the second derivative is negative?[br][/list][br][/list]