304
The disadvantage of the previous method is that it is not very visual. An
alternative is to use the “Chords” aplet.
In this aplet, a menu is provided via
the VIEWS menu to allow students to
choose from a list of predefined
functions or enter their own. Once
the function has been graphed, the ‘Show slopes’ option
will display an animated series of chords of diminishing
length, with the gradient displayed at the top of the
screen. As the chord shortens the student can see how
this affects the approximation to the gradient at the point chosen.
G
G
r
r
a
a
d
d
i
i
e
e
n
n
t
t
F
F
u
u
n
n
c
c
t
t
i
i
o
o
n
n
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 using an aplet
downloaded from The HP HOME View web site called
“Tangent Lines”. This aplet will add a moveable tangent line to a graph,
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.
If it is not desirable to use this aplet then the Statistics aplet can be used to
help with the process of finding gradient functions once tabular data has
been collected giving x and grad(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 function and then use the curve fitting facilities to find an
equation.
Curves of the form
ymxb
+ ,
2
yax bxc=++,
32
yax bx cxd
+++ and
b
yax= can
be fitted using the Statistics aplet and this should be enough for the students
to deduce the rule
)
1
n
n
dx
nx
dx
−
= for themselves. It 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.
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