HP 15c - Manual (Page 233)

Appendix D: A Detailed Look at _ 233
Keystrokes Display
´ _.0 Error 8
− 1.0000 –20 Best x-value.
) 1.1250 –20 Previous value.
) 2.0000
Function value.
| (| ( 1.0000 –20 Restore the stack.
´ _ .0 Error 8
− 1.1250 –20 Another x-value.
) 1.5626 –16 Previous value.
) 2.0000
Same function value.
In each of the three cases, _ initially
searched for a root in a direction suggested by
the graph around the initial estimate. Using
10 as the initial estimate, _ found the
horizontal asymptote (value of 1.0000).
Using 1 as the initial estimate, a minimum of
0.3788 at x = 2.1213 was found. Using 10
–20
as the initial estimate, the function was
essentially constant (at a value of 2.0000) for
the small range of x that was sampled.
Finding Several Roots
Many equations that you encounter have more than one root. For this
reason, you will find it helpful to understand some techniques for finding
several roots of an equation.
The simplest method for finding several roots is to direct the root search in
different ranges of x where roots may exist. Your initial estimates specify
the range that is initially searched. This method was used for all examples
in section 13. You can often find the roots of an equation in this manner.
Another method is known as deflation. Deflation is a method by which roots are
"eliminated" from an equation. This involves modifying the equation so that the
first roots found are no longer roots, but the rest of the roots remain roots.
If a function f(x) has a value of zero at x = a, then the new function
f(x)/(x – a) will not approach zero in this region (if a is a simple root of
f(x) = 0). You can use this information to eliminate a known root. Simply