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Nilai maksimum dari fungsi f(x) = 2cos 2 x + 4cos x + 6 sin 2 x adalah ....

Nilai maksimum dari fungsi f(x) = 2cos2 x + 4cos x + 6 sin2 x adalah ....

  1. 8

  2. 7

  3. 6

  4. 5

  5. 4

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

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Pembahasan

straight f open parentheses straight x close parentheses equals 2 cos squared straight x plus 4 cos space straight x plus 6 sin squared straight x  straight f open parentheses straight x close parentheses equals 2 cos squared straight x plus 4 cos space straight x plus 6 open parentheses 1 minus cos squared straight x close parentheses  straight f open parentheses straight x close parentheses equals 2 cos squared straight x plus 4 cos space straight x plus 6 minus 6 cos squared straight x  straight f open parentheses straight x close parentheses equals negative 4 cos squared straight x plus 4 cos space straight x plus 6    Perhatikan space bahwa space titik space ekstrem space fungsi space memenuhi  straight f apostrophe open parentheses straight x close parentheses equals 0  minus 4 left parenthesis 2 cos space straight x right parenthesis open parentheses negative sin space straight x close parentheses plus 4 open parentheses negative sin space straight x close parentheses equals 0  8 cos space straight x. sin space straight x minus 4 sin space straight x equals 0  4 sin space straight x open parentheses 2 cos space straight x minus 1 close parentheses equals 0  Pembuat space nol space colon space box enclose sin space straight x equals 0 end enclose space atau space box enclose cos space straight x equals 1 half end enclose.    Pada space interval space 0 less or equal than straight x less or equal than 360 degree comma  sin space straight x equals 0 rightwards arrow box enclose straight x equals 0 degree comma 180 degree comma 360 degree end enclose  cos space straight x equals 1 half rightwards arrow box enclose straight x equals 60 degree comma 300 degree end enclose    Substitusikan space titik minus titik space tersebut space ke space straight f open parentheses straight x close parentheses equals negative 4 cos squared straight x plus 4 cos space straight x plus 6 comma  straight x equals 0 degree rightwards arrow straight f open parentheses straight x close parentheses equals negative 4 open parentheses 1 close parentheses squared plus 4 open parentheses 1 close parentheses plus 6 equals 6  straight x equals 60 degree rightwards arrow straight f open parentheses straight x close parentheses equals negative 4 open parentheses 1 half close parentheses squared plus 4 open parentheses 1 half close parentheses plus 6 equals 7  straight x equals 180 degree rightwards arrow straight f open parentheses straight x close parentheses equals negative 4 open parentheses negative 1 close parentheses squared plus 4 open parentheses negative 1 close parentheses plus 6 equals negative 2  straight x equals 300 degree rightwards arrow straight f open parentheses straight x close parentheses equals negative 4 open parentheses 1 half close parentheses squared plus 4 open parentheses 1 half close parentheses plus 6 equals 7  straight x equals 360 degree rightwards arrow straight f open parentheses straight x close parentheses equals negative 4 open parentheses 1 close parentheses squared plus 4 open parentheses 1 close parentheses plus 6 equals 6    Didapat space nilai space maksimum equals box enclose 7.

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