| What do these
differences look like when plotted on a
graph? |
First, ensure the list display
has 1, 2, 3, 4, 5, 6, 7 in L1 and the cube numbers 1, 8, 27, 64... in L2, and
the first second and third differences in L3, L4 and L5 respectively. See
Section 4 on how to enter differences.
Before displaying scatter graphs
of the differences, the size of the lists in L3, L4 and L5 need to be made the
same as L1. Can you figure out what the differences needed to complete L3, L4
and L5 are? Go to STAT EDIT and make L3(7)=169, L4(6) = 42. L4(7)=48,
L5(5)=6, L5(6)=6, L5(7)=6.
Set up your calculator as in Section 5 to display a scatter graph of (L1,L2). Then
display scatter graphs of (L1,L3), (L1,L4) and (L1,L5).
Do the same for other sequences based
on the cubes. The four curves obtained are always cubic, quadratic, linear and
constant curves. If you study A-Level mathematics you will see a connection
here between differences and differentiation. In calculus, if f(x) =
x3, then f'(x) = 3x2, f''(x) = 6x and f'''(x) =
6.
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