HP -32S Owner's Manual page 262

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