find the maximum of the function f ( x ) = a + b <msqrt> 2 </msq

Wisniewool

Wisniewool

Answered question

2022-07-10

find the maximum of the function f ( x ) = a + b 2 sin x + c sin 2 x , 0 < x < π 2

Answer & Explanation

amanhantmk

amanhantmk

Beginner2022-07-11Added 17 answers

Use Cauchy-Schwarz inequality:
( a + b 2 sin x + c sin 2 x ) 2 ( a 2 + b 2 + c 2 ) ( 1 + 2 sin 2 x + sin 2 2 x )
( a + b 2 sin x + c sin 2 x ) 2 100 ( 1 + 2 sin 2 x + sin 2 2 x )
| a + b 2 sin x + c sin 2 x | 10 1 + 2 sin 2 x + sin 2 2 x
1 1 + 2 sin 2 x + sin 2 2 x 13 4
Then
5 13 a + b 2 sin x + c sin 2 x 5 13

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