132e6adb-1306-4939-9c64-797d37cd2977 26 4 5 false false 0 decimal

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

o Extremes auxiliary function

x y Extremes 1 m E x y augment eval y m eval 2 findrows 11 line : x# min E x# max E 12 mat eval 21 line :

Find the max

Function

x f 1 x 2^- :

x f

Interval of interest

a b 12 mat 2 - 212 mat :

o Brute force method

N 100 : n 1 N range : 12 mat X n el a b a - N 1 - / n 1 - (* + : Y n el X n el f : 12 mat xy.m xy.M 12 mat X Y Extremes : 31 line

X Y augment xy.M o augment 2 1 sys

This method gives two approx results:

xy.M 0.0202 - 0.9996 0.0202 0.9996 22 mat

o Critical Points method

x df x f x diff : x.c x df x a b solve a b stack : xy.m xy.M 12 mat x.c x.c f vectorize Extremes : 31 line

x f xy.M o augment 2 1 sys

This method is more precise:

xy.M 0112 mat

o The Critical Points method by "hand"

Derivative

x df x f x diff : 2 x * -

Zeros of the der

x.z x df x a b solve :

Singularities of f

x.σ 01 matrix :

(None)

Critical points

x.c x.z x.σ a b stack :

x.c transpose 02 - 213 mat

y.c x.c f vectorize :

Maximum

y.M y.c max eval :

y.M 1

Where the max occur and the max.

xy.M x.c y.c augment eval y.M 2 findrows : 0112 mat

Alvaro