HP HP-15C

Section 1: Using [SOLVE] Effectively
f(x)
If [SOLVE [has already found values a and b such that/(a) an
have opposite signs, it modifies the secant method to ensure that c
always lies within the interval containing the sign change. This
guarantees that the search interval decreases with each iteration,
eventually finding a root.
f(x)
b /
If | SOLVE | hasn't found a sign change and a sample value c doesn't
yield a function value with diminished magnitude, then | SOLVE | fits
a parabola through the function values at a, b, and c. \E | finds
the value d at which the parabola has its maximum or minimum,
relabels d as a, and then continues the search using the secant
method.