Найдите наибольшее значение функции y = 16tgx−16x+4π−5 на отрезке [−π/4;π/4]. Created by lianadyusmetova. algebra-ru

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July 2022 1 7 Report

Найдите наибольшее значение функции y = 16tgx−16x+4π−5 на отрезке [−π/4;π/4]

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mikael2 Y=16tgx-16x+4π-5 i=[-π/4;π/4]
y'=16/cos²x-16 y'=0 1/cos²x=1
cosx=1 cosx=-1 x=πk k∈Z
k=0 x=0 y=4π-5

x=-π/4 y=-16+4π+4π-5=8π-21
x=π/4 y=16-4π+4π-5=11
8π-21-11=8π-32 8π-21<11
4π-5-8π+21=-4π+16>0

min 8π-21

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