HP 35s User Manual page 324

If f(x) has one or more local minima or minima, each occurs singly between
adjacent roots of f(x) (figure d, below).
f (x)
a
f (x)
c
Function 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 f(x) = 0.
However, a very small non–zero value for f(x) is often acceptable because it might
result from approximating numbers with limited (12–digit) precision.
D-2
More about Solving
x
x
f (x)
b
f (x)
d
x
x