<content> <p> Golden ratio min/max </p> </content>

d4f7c914-2498-4dc1-8619-814098c92213 9 4 5 false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

x y axes x y / - :

Golden-Ratio [min/max]... roots

Code adapted from  Mathcad 11 f a b test TOL Extrema a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / 71 line :

a b + 2 / iter 21 mat

y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ 21 sys

x f x 4^2 x 3^* - 7 x 2^* - 2 - eval :

ε 1015 -^:

By setting f(x):=eval(,)by default, it will cope with all "_not defined"
As well, you may have to use local definition.
Some functions will ONLY accept higher 'ε' ... 10^{-14} ... 10^{-13}

t0 1 time :

rootsDichotomy local command line style x0 x1 TOL D a x0 : b x1 : 12 mat xn b a + (2 / : ε TOL : 12 mat 21 sys n 0 : xn f abs ε > xn f a f * 0 ≤ b xn : a xn : if xn b a + (2 / : n n 1 + : 31 line while xn 21 line 31 line :

X f 1.5 - 1 - y1 y2 ≤ ε Extrema f 0.5 - 0.5 y1 y2 ≥ ε Extrema f 2.5 3 y1 y2 ≤ ε Extrema 31 mat :

1 time t0 - 0.5 s *

on failure , increase TOL TOL 1012 -^:

r 2.5 - 1.5 - TOL D 3.5 4 TOL D 21 mat : 1.922518473318 - 3.852153430325 21 mat

X 1.26556446000827 - 2.81605475000001 108 -^* - 2.76556437660309 31 mat

plot x f axes X 1 el X 1 el f + 20 red X 2 el X 2 el f + 20 red X 3 el X 3 el f + 20 red 35 mat r 1 el 0.4 black 15 mat r 2 el 0.4 black 15 mat 51 sys :

plot

X f vectorize 6.5923 - 2 - 39.3452 - 31 mat