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

c98c9033-1bb0-4f70-a1c1-cb043c71bb89 23 4 5 decimal

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f.n k Q M k f.n 2^* 1 k + (f.n 2^* 1 - (2^Q k * f.n * f.n 2^1 - (2^* + sqrt / :

Target: 1. The plot is just required the first quadrant.2. Find the value of fn when M is maximum3. Find the maximum value of M

f.n 5 0.5 M

f.n1 f.n 5 0.5 M f.n diff f.n 0.4 roots : #

f.n1 5 0.5 M #

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f.n k Q M k f.n 2^* 1 k + (f.n 2^* 1 - (2^Q k * f.n * f.n 2^1 - (2^* + sqrt / f.n 0 ≥ (f.n 2 ≤ (& cases :

f.n 5 0.5 M

f.n 5 0.5 M f.n diff f.n 0.4 0.6 solve #

f.n 5 0.5 M f.n diff f.n 0.4 roots #

f.n k Q M k f.n 2^* 1 k + (f.n 2^* 1 - (2^Q k * f.n * f.n 2^1 - (2^* + sqrt / f.n 0 ≥ (f.n 2 ≤ (& cases :

k 5 :

Q 0.5 :

x f k x 2^* 1 k + (x 2^* 1 - (2^Q k * x * x 2^1 - (2^* + sqrt / :

x f <p> Golden ratio min/max </p>

Code adapted from Valery Ochov 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 k x 2^* 1 k + (x 2^* 1 - (2^Q k * x * x 2^1 - (2^* + sqrt / eval :

ε 1015 -^:

X f 0.4 0.6 y1 y2 ≥ ε Extrema :

X 0.5462

You may have to lower 'ε' ... 10^-12

X f 1.3101