Math problem where graphing calculator may slow you down - part II.

[Thomas Klemm]

(11-30-2014 01:33 AM)lrdheat Wrote:  Rather slow on this sort of problem!

For this specific problem the derivative is trivial:

\[
\begin{align}
F(x)&=\int_{0}^{x}f(t)dt-4 \\
F'(x)&=f(x) \\
\end{align}
\]

Thus we can use Newton's method:
\[
\begin{align}
x'&=x-\frac{F(x)}{F'(x)} \\
&=x-\frac{\int_{0}^{x}f(t)dt-4}{f(x)} \\
&=x+\frac{\int_{x}^{0}f(t)dt+4}{f(x)} \\
\end{align}
\]

Instead of starting the integration from \(0\) over and over again we can reuse the result of \(F(x)\) from the previous loop:
\[
F(x')=F(x)+\int_{x}^{x'}f(t)dt
\]
This value is saved in register 01.

Code:

LBL'FX'
# 001
→REC
MAX
RTN

Code:

LBL'NWT'
# 004
STO 01
CLx
STO 00
R↓
LBL 00
ENTER↑
x<> 00
∫'FX'
RCL+ 01
STO 01
RCL 00
XEQ'FX'
/
x≈0?
SKIP 002
RCL+ 00
GTO 00
RCL 00
END

This will speed up the calculation.

Cheers
Thomas