Знайдіть екстремум функції y=sin^22x на проміжку [ π/6; π/3 ].. Created by tanyagolub1982. algebra-ru

Наибольшее значение в точке равно 1

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tanyagolub1982 @tanyagolub1982

July 2022 1 8 Report

Знайдіть екстремум функції y=sin^22x на проміжку [ π/6; π/3 ].

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nafanya2014

Verified answer

$sin^22x=\frac{1-cos4x}{2}$

$y`=(\frac{1-cos4x}{2})`=\frac{1}{2}(1-cos4x)`=\frac{1}{2}(0-(-sin4x)\cdot (4x)`)=2sin4x$

$y`=0\\\\sin4x=0\\\\4x=\pi k, k \in Z\\\\x=\frac{\pi k}{4} , k \in Z\\\\\frac{\pi}{4} \in [\frac{\pi}{6};\frac{\pi}{3}]$

$y(\frac{\pi}{4})=sin^2(2\cdot \frac{\pi}{4})=sin^2\frac{\pi}{2}=1$

Наибольшее значение в точке

$x=\frac{\pi}{4}$

равно 1

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Answers & Comments

Verified answer

znajdit vidstan vid centra kola do hordi yaksho vona diametrom podilyayetsya na v

chisla m n i k prosti skilki riznih dilnikiv maye chislo mn4k n v chetve

cherez vershinu k gostrokutnogo trikutnika nkp proveli pryamu perpendikulyarnu do s

vidomo sho h u 4 chomu dorivnyuye vidnoshennya 9h 2u

4 pershogo chlena znajdit chetvertij chlen proporciyi

peremnozhili dekilka naturalnih chisel i otrimali 184 skilki chisel peremnozhili

yakih znachen mozhe nabuvati viraz cos a 05

chi mozhna opisati cilindr navkolo pryamoyi prizmi osnovoyu yakoyi ye pryamokutnij triku

serednye znachennya vibirki yaka skladayetsya iz desyati elementiv dorivnyuye 17 do v

dva kola mayut radiusi 123 sm i 59 sm yakogo najbilshogo cilogo znachennya vira

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