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Diketahui fungsi g ( x ) = 3 1 ​ x 3 − 9 A 2 ​ x + 1 , A konstanta . Jika f ( x ) = g ( 2 x − 1 ) dan f naik pada x ≤ 0 atau x ≥ 1 , nilai maksimum relatif g adalah ...

  1. 7 over 3

  2. 5 over 3

  3. 1 third

  4. negative 1 third

  5. negative 5 over 3

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F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

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Pembahasan

Misal comma space straight k squared equals straight A squared over 9  sehingga space straight g left parenthesis straight x right parenthesis equals 1 third straight x cubed minus straight k squared straight x plus 1    straight f left parenthesis straight x right parenthesis equals straight g left parenthesis 2 straight x minus 1 right parenthesis  equals 1 third left parenthesis 2 straight x minus 1 right parenthesis cubed minus straight k squared left parenthesis 2 straight x minus 1 right parenthesis plus 1  equals 8 over 3 straight x cubed minus 4 straight x squared plus left parenthesis 2 minus 2 straight k squared right parenthesis straight x plus left parenthesis straight k squared plus 2 over 3 right parenthesis  rightwards double arrow straight f to the power of apostrophe left parenthesis straight x right parenthesis equals 8 straight x squared minus 8 straight x plus left parenthesis 2 minus 2 straight k squared right parenthesis  straight f left parenthesis straight x right parenthesis space naik space pada space straight x less or equal than 0 space atau space straight x greater or equal than 1 comma space maka space akar minus akar space persamaan space straight f to the power of apostrophe left parenthesis straight x right parenthesis space adalah space straight x subscript 1 equals 0 space dan space straight x subscript 2 equals 1 comma space sehingga  straight x subscript 1 straight x subscript 2 equals fraction numerator 2 minus 2 straight k squared over denominator 8 end fraction  0 equals fraction numerator 2 minus 2 straight k squared over denominator 8 end fraction  0 equals 2 minus 2 straight k squared  2 straight k squared equals 2  straight k squared equals 1 rightwards arrow straight k squared equals straight A squared over 9  straight g left parenthesis straight x right parenthesis equals 1 third straight x cubed minus straight x plus 1  straight g apostrophe left parenthesis straight x right parenthesis equals straight x squared minus 1 space    Cari space titik space stasioner space fungsi  straight g apostrophe left parenthesis straight x right parenthesis equals 0  straight x squared minus 1 equals 0  left parenthesis straight x plus 1 right parenthesis left parenthesis straight x minus 1 right parenthesis equals 0  straight x equals negative 1 logical or straight x equals 1    Untuk space straight x equals negative 1 space colon  straight g left parenthesis negative 1 right parenthesis equals 1 third left parenthesis negative 1 right parenthesis cubed minus left parenthesis negative 1 right parenthesis plus 1 equals negative 1 third plus 1 plus 1 equals 5 over 3 rightwards arrow box enclose maksimum  Untuk space straight x equals 1 space colon  straight g left parenthesis 1 right parenthesis equals 1 third left parenthesis 1 right parenthesis cubed minus 1 plus 1 equals 1 third    Sehingga space nilai space maksimum space relatif space straight g space adalah space 5 over 3.

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Tentukan nilai maksimum dan minimumnya 1. f ( x ) = x 3 − 3 x 2 − 9 x + 2 , − 2 ≤ x ≤ 4

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