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Консультация № 159926
08.02.2009, 13:50
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Здравтсвуйте! Помогите пожалуйста найти наибольшее и наименьшее значение функции y=f(x) на отрезке [a;b]
f (x)= (корень квадратный из 3/2)х+cosx ; [0;П/2]
f (x)= (корень квадратный из 3/2)х+cosx ; [0;П/2]
Обсуждение
Неизвестный
08.02.2009, 15:20
общий
это ответ
Здравствуйте, Попова Елена Сергеевна!
f(x)=sqrt3/2*x+cosx
f(0)=1
f(pi/2)=pi*sqrt3/4~1.36
f'(x)=sqrt3/2-sinx
f'(x)=0
sqrt3/2-sinx=0
sinx=sqrt3/2
x=pi/3+2*pi*n
x=2*pi/3+2*pi*n
Отрезку [0, pi/2] принадлежит х=pi/3
f(pi/3)=sqrt3/2*pi/3+1/2=(pi+sqrt3)/(2*sqrt3)~1.4
Наименьшее значение функции при х=0
f(0)=1
Набольшее при х=pi/3
f(pi/3)=(pi+sqrt3)/(2*sqrt3)
f(x)=sqrt3/2*x+cosx
f(0)=1
f(pi/2)=pi*sqrt3/4~1.36
f'(x)=sqrt3/2-sinx
f'(x)=0
sqrt3/2-sinx=0
sinx=sqrt3/2
x=pi/3+2*pi*n
x=2*pi/3+2*pi*n
Отрезку [0, pi/2] принадлежит х=pi/3
f(pi/3)=sqrt3/2*pi/3+1/2=(pi+sqrt3)/(2*sqrt3)~1.4
Наименьшее значение функции при х=0
f(0)=1
Набольшее при х=pi/3
f(pi/3)=(pi+sqrt3)/(2*sqrt3)
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