f(x)
always increases or always decreases as x increases (figure b,
below).
The graph of
f(x)
is either concave everywhere or convex every
where (figure c, below).
If
/fa)
has one or more local minima or maxima, each occurs singly
between adjacent roots of
/fa)
(figure d, below).
Functions
Whose
Roots
Can
Be
Found
In
most
situations,
the
calculated
root
is
an
accurate
estimate
of
the
theoretical, infinitely precise root of the equation. An
'ideal'
solution
is one for which /fa)=0. However, a very small non-zero value for /fa)
is often acceptable because it might result from approximating num
bers with limited (12-digit) precision.
260
C:
More
About
Solving
an
Equation
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