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mkineshma
@mkineshma
July 2022
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Найти наибольшее и наименьшее значение функции на отрезке
[tex]y= \frac{ \sqrt{3} }{2} x-cosx
(- \pi ; \pi )[/tex]
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lexusenok
Y'(х)=\/(3)/2 +sinx
y'(х)=0
\/(3)/2 +sinx=0
sinx=-\/(3)/2
x=-п/3+2пn, n - целое число
х=-2п/3+2пk, k - целое число
-п<=х<=п
х=-п/3
х=-2п/3
у(-п)=-п\/(3)/2 +1=(2-п\/(3))/2
у(п)=(2+п\/(3))/2
у(-п/3)=-п\/(3)/6 -1/2=-(3+п\/(3))/6
у(-2п/3)=-п\/(3)/3 +1/2=(3-2п\/(3))/6
На -п<=х<=п
унаиб.=у(п)=(2+п\/(3))/2
унаим.=у(-п)=(2-п\/(3))/2
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Answers & Comments
y'(х)=0
\/(3)/2 +sinx=0
sinx=-\/(3)/2
x=-п/3+2пn, n - целое число
х=-2п/3+2пk, k - целое число
-п<=х<=п
х=-п/3
х=-2п/3
у(-п)=-п\/(3)/2 +1=(2-п\/(3))/2
у(п)=(2+п\/(3))/2
у(-п/3)=-п\/(3)/6 -1/2=-(3+п\/(3))/6
у(-2п/3)=-п\/(3)/3 +1/2=(3-2п\/(3))/6
На -п<=х<=п
унаиб.=у(п)=(2+п\/(3))/2
унаим.=у(-п)=(2-п\/(3))/2