HP 40gs HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 319

The Chain Rule If desirable, an aplet is available from The HP HOME View web site (at http://www.hphomeview.com), called "Chain Rule", which will encourage the student to deduce the Chain Rule for themselves. It is pre-loaded with five sets of functions, of increasing complexity, the first three of which are shown right. The functions are loaded into F1, F3, F5, F7 and F9, while the functions F2, F4, F6, F8 and F0 contain an expression which, when is pressed, will differentiate the function above. Through the worksheet which is bundled with the aplet, the student is directed to record the functions and their derivatives and to look for patterns which will allow them to deduce a rule. Obviously the student could simply type these functions in themselves but it would be very tedious and the aplet automates the process so as not to obscure the learning. Optimization A method which I find to be efficient in introducing the idea of optimization is via the maximization of the volume of an open-topped box. If we start with a sheet of card which is 15cm by 11cm then we can form a box by removing squares from the corners and folding up the sides. I find that it is quite helpful for the students to actually make such a box, choosing for themselves what size square to cut out. They can then explore, using the Function aplet, what cut-out size will produce the maximum volume. As can be seen above & right, the width, length and height can be entered into F1, F2 and F3 as functions of the cut-out size X. The volume can then be entered into F4 as F4(X)=F1*F2*F3 and this function can then be plotted and the maximum found either through successive approximations in the NUM view or by using the FCN tools in the PLOT view. 319