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Консультация № 110017
18.11.2007, 17:19
0.00 руб.
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Здравствуйте эксперты, помогите с задачкой:
функция f(x) определена на [0,1] причем f(0)=f(1)=0 и сущесвует x, y принадлежит [0,1] верно неравество f((x+y)/2)<f(x)+f(y) докажите что функция f(x) имеет бессконечное число нолей
функция f(x) определена на [0,1] причем f(0)=f(1)=0 и сущесвует x, y принадлежит [0,1] верно неравество f((x+y)/2)<f(x)+f(y) докажите что функция f(x) имеет бессконечное число нолей
Обсуждение
Неизвестный
19.11.2007, 10:54
общий
это ответ
Здравствуйте, Tribak!
Здравствуйте эксперты, помогите с задачкой:
функция f(x) определена на [0,1] причем f(0)=f(1)=0 и сущесвует x, y принадлежит [0,1] верно неравество f((x+y)/2) < f(x)+f(y) докажите что функция f(x) имеет бессконечное число нолей
Мне кажется, что где-то в задании ошибка, так как такой функции, как описана, не может быть.
f(1/2) < f(0) + f(1) = 0
f(1/4) < f(0) + f(1/2) = f(1/2)
f(3/4) < f(1/2) + f(1) = f(1/2)
Но
f(1/2) < f(1/4) + f(3/4) < 2*f(1/2) => f(1/2) > 0, что противоречит первому неравенству.
Здравствуйте эксперты, помогите с задачкой:
функция f(x) определена на [0,1] причем f(0)=f(1)=0 и сущесвует x, y принадлежит [0,1] верно неравество f((x+y)/2) < f(x)+f(y) докажите что функция f(x) имеет бессконечное число нолей
Мне кажется, что где-то в задании ошибка, так как такой функции, как описана, не может быть.
f(1/2) < f(0) + f(1) = 0
f(1/4) < f(0) + f(1/2) = f(1/2)
f(3/4) < f(1/2) + f(1) = f(1/2)
Но
f(1/2) < f(1/4) + f(3/4) < 2*f(1/2) => f(1/2) > 0, что противоречит первому неравенству.
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