More
About
Solving
an
Equation
c
This appendix provides information about the
SOLVE
operation be
yond that given in chapter 7.
How
SOLVE
Finds
a
Root
SOLVE
is an
iterative
operation; that is, it repetitively executes the
specified function. It starts with an estimate for the unknown vari
able,
x,
and
refines
that
estimate
with
each
successive
execution
of
the
function,
f(x).*
If any two successive estimates of the function
f(x)
have opposite
signs, then
SOLVE
presumes that the function
f(x)
crossesthe x-axisin
at least one place between the two estimates. This interval is sys
tematically narrowed until a root is found.
For
SOLVE
to find a root, the root has to exist within the range of
numbers of
the
calculator,
and
the function must be mathematically
defined where the iterative search occurs.
SOLVE
always finds a root,
provided one exists (within the overflow bounds), if one or more of
these
conditions
are
met:
• Two estimates yield /fa) values with opposite signs,
and
the
function's graph crosses the
jc-axis
in at least one place between
those estimates (figure a, next page).
•/fa) is mathematical shorthand for a function defined in terms of the unknown variable x.
C:
More
About
Solving
an
Equation
259
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