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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
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.
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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 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.
is pressed, will differentiate the function above. Through
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