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Jika nilai maksimum dan minimum fungsi f ( x ) = a cos ( x ) + b berturut-turut adalah 6 dan 2, maka nilai minimum fungsi g ( x ) = 2 a sin ( x ) + 3 b adalah ....

Jika nilai maksimum dan minimum fungsi berturut-turut adalah 6 dan 2, maka nilai minimum fungsi  adalah ....

  1. -4

  2. -2

  3. 2

  4. 4

  5. 8

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Pembahasan

Diketahui space straight f left parenthesis straight x right parenthesis equals straight a space cos left parenthesis straight x right parenthesis plus straight b  Karena space minus 1 less or equal than cos space straight x less or equal than 1 comma space maka space box enclose negative vertical line straight a vertical line plus straight b less or equal than straight f left parenthesis straight x right parenthesis less or equal than vertical line straight a vertical line plus straight b end enclose    Karena space nilai space maksimum space straight f left parenthesis straight x right parenthesis equals 6 space dan space nilai space minimum space straight f left parenthesis straight x right parenthesis equals 2 comma space maka space  minus vertical line straight a vertical line plus straight b equals 2 space  vertical line straight a vertical line plus straight b equals 6 space  Dengan space eliminasi space akan space didapat space box enclose vertical line straight a vertical line equals 2 end enclose space dan space box enclose straight b equals 4 end enclose.    Misalkan space straight g left parenthesis straight x right parenthesis equals straight a space sin invisible function application straight x plus straight b  Karena space minus 1 less or equal than sin invisible function application straight x less or equal than 1 comma space maka space box enclose negative vertical line straight a vertical line plus straight b less or equal than straight g left parenthesis straight x right parenthesis less or equal than vertical line straight a vertical line plus straight b space space end enclose    Diketahui space straight g left parenthesis straight x right parenthesis equals 2 straight a space sin invisible function application straight x plus 3 straight b space  Maka space  minus vertical line 2 straight a vertical line plus 3 straight b less or equal than straight g left parenthesis straight x right parenthesis less or equal than vertical line 2 straight a vertical line plus 3 straight b space  minus 2 vertical line straight a vertical line plus 3 straight b less or equal than straight g left parenthesis straight x right parenthesis less or equal than 2 vertical line straight a vertical line plus 3 straight b space  minus 2 left parenthesis 2 right parenthesis plus 3 left parenthesis 4 right parenthesis less or equal than straight g left parenthesis straight x right parenthesis less or equal than 2 left parenthesis 2 right parenthesis plus 3 left parenthesis 4 right parenthesis space  space space space space space space space minus 4 plus 12 less or equal than straight g left parenthesis straight x right parenthesis less or equal than 4 plus 12 space  space space space space space space space space space space space space space space space space space space space box enclose 8 less or equal than straight g left parenthesis straight x right parenthesis less or equal than 16 end enclose space    Didapatkan space nilai space minimum space fungsi space straight g left parenthesis straight x right parenthesis space adalah space box enclose 8.

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Gambarlah grafik fungsi y = 2 sin x + 1 dan y = 2 cos x + 1 untuk 0 ∘ ≤ x ≤ 36 0 ∘ pada satu bidang koordinat!

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4.4

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