tex] на отрезке [-5; 5]...

regginanikolenko @regginanikolenko

July 2022 1 12 Report

50 БАЛЛОВ Найти наибольшее и наименьшее значения функции [tex]y=\frac{x-3}{x^2+16}}[/tex] на отрезке [-5; 5]

Answers & Comments

NNNLLL54

Verified answer

Ответ:

$y_{min}=-\dfrac{1}{4}\ ,\ \ y_{max}=\dfrac{1}{16}\ ,\\\\y_{naimen.}=-\dfrac{8}{41}\ \ ,\ \ y_{naibol.}=\dfrac{2}{41}$ .

Решение.

$y=\dfrac{x-3}{x^2+16}\ \ ,\ \ x\in [-5\ ;\ 5\ ]\\\\\\y'=\dfrac{x^2+16-(x-3)\cdot 2x}{(x^2+16)^2}=\dfrac{-x^2+6x+16}{(x^2+16)^2}=0\ \ \Rightarrow \ \ \ -x^2+6x+16=0\\\\\\x^2-6x-16=0\ \ ,\ \ \ x_1=-2\ ,\ x_2=8\ \ \ (teorema\ Vieta)\\\\\\\dfrac{-(x+2)(x-8)}{(x^2+16)^2}=0\\\\\\znaki\ y'(x):\ \ \ ---(-2)+++(8)---\\{}\qquad \qquad \qquad \quad \ \searrow \, \ \ (-2)\ \ \nearrow \ \ \ (8)\ \ \searrow \\{}\qquad \qquad \qquad \qquad \qquad min\ \ \ \qquad max$

$x_{min}=-2\ \ ,\ \ y_{min}=y(-2)=\dfrac{-2-3}{4+16}=-\dfrac{5}{20}=-\dfrac{1}{4}\ \ ,\ \ -2\in [-5\ ;\ 5\ ]\\\\\\x_{max}=8\ \ ,\ \ \ y_{max}=y(8)=\dfrac{8-3}{64+16}=\dfrac{5}{80}=\dfrac{1}{16}\ ,\ \ 8\notin [-5\ ;\ 5\ ]\\\\y(-5)=\dfrac{-8}{41}\ \ ,\ \ y(5)=\dfrac{2}{41}\\\\\\-\dfrac{8}{41}$

3 votes Thanks 2

Answers & Comments

Verified answer

pomogite nuzhny kody na pitone dlya 3 zadanij 1 najti kolichestvo elementov massacc6f3a29b1b65cf123e4f918874fd2e 37404

pomogite s kodom na python zadacha1 kolichestvo elementov mezhdu minimumom i maks

100 ballov nuzhno napisat programmu na pythone kotoraya po vvedennomu znacheniyu

tex]...

tex]...

tex na otrezke 5 5

tex]...

yazyk programmirovaniya piton nuzhno napisat programmu na pythone kotoraya oprede

pomogite nuzhny kody na pitone dlya 3 zadanij 1 najti kolichestvo elementov mass

рекомендуемые вопросы

Helpful Links

Helpful Social