297436e4-7150-4760-9cdd-6c701e6a140d 4 4 5 decimal

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

x F x f x g * :

x dF.m x f x g * x diff maple : x f x diff x g * x f x g x diff * +

x dF x dF.m num2str diff(g(x),x) 0 strrep g(x) hs(x) strrep str2num eval :

x f x :

b 0.625 :

x f x diff 1

symbolic results

x Bolean x b ≥ (:

x g x Bolean :

x F x x 58 / ≥ *

x hs x 0.5 > :

Lo w Int x F x Lo w int :

1 - 2 Int 1.8047

b 2 Int 1.8047

Simpson integrator is known inaccurate for linear functions. Options,Accuracy 10000

x F x f x diff x Bolean * 2 1 sys

0 F 0

b F 0.625

Algo style Memo formula of incremental analysis of this demo example h 0.01 : (increment ≡ x h f deriv 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* : x h f D1 x 2 h * + f - 8 x h + f * + 8 x h - f * - x 2 h * - f + 12 h * / : (1rst Derivative ≡ x h f D2 x 2 h * + f - 16 x h + f * + 30 x f * - 16 x h - f * + x 2 h * - f - 12 h 2^* / : (2nd Derivative ≡ x h D3 x 3 h * - f 8 x 2 h * - f * - 13 x h - f * + 13 x h + f * - 8 x 2 h * + f * + x 3 h * + f - 8 h 3^* / : x h D4 x 3 h * - f - 12 x 2 h * - f * + 39 x h - f * - 56 x f * + 39 x h + f * - 12 x 2 h * + f * + x 3 h * + f - 6 h 4^* / : x h f h_int h x h + f x f - (* 2 x f * + (x * : (Integral Curve [antiderivative] ≡ 71 line

x f x F :

x D x h f D1 x Bolean * :

x F x D 2 1 sys