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F
F
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Once the concept of gradient at a point has been established the
next step is to develop the idea of a gradient function. This can be
done via the Function aplet by using the
Slope function which
gives the gradient of the graph at the position of the cursor (see page
58).
If the teacher has the student enter a function in the SYMB view they
can then have the student explore the value of the slope at various values using the
function to position
the cursor precisely.
The Statistics aplet can be used to help with the process of finding gradient functions once tabular data has
been collected giving x and slope(x) values. If the student enters the data into
C1 and C2, they can then set
to
, plot the data and make a guess as to the appropriate type of function in the SYMB SETUP view
and then use the curve fitting facilities to find an equation.
3
+
2
= +
2
+ + + + =
Curves of the form
ymxb,
= ax bx c ,
ax bx cx d and yax
b
can be fitted using the
dx
n
)
Statistics aplet and this should be enough for the students to deduce the rule
=
nx
n−1
for themselves. It
dx
is advisable to ensure that the students are familiar with the process of using the Statistics aplet to find
equations before commencing, otherwise the two concepts may interfere and confuse.
The process can be done in a far more visual style using an aplet downloaded from The HP HOME View web
site (http://www.hphomeview.com
) c
alled “Tangent Lines”. This aplet will add a moveable tangent line to an
existing graph, as shown in the screen shot above, allowing the user to move it along the curve with the
gradient displayed at the top left of the screen. There are two worksheets included in the documentation
which is bundled with this aplet which will take the student through the process of developing a gradient
function.
318
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