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Pertanyaan

Fungsi f ( x ) = x 3 − 2 3 ​ x 2 naik pada interval….

Fungsi  naik pada interval ….

  1. x less than 0 space dan space x greater than 1 space

  2. 0 less than x less than 1

  3. x less than negative 1 space dan space x greater than 0 space

  4. negative 1 less than x less than 1

  5. x less than 1 space dan space x greater than 2

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A. Nadhira

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

fungsi naik pada interval .

fungsi f left parenthesis x right parenthesis equals x cubed minus 3 over 2 x squared naik pada interval x less than 0 space dan space x greater than 1 space.

Pembahasan

Fungsi naik, maka: Kemudian uji nilai f'(x) pada x = -1, x = , dan x = 2, sehingga diperoleh garis bilangan sebagai berikut. Jadi, fungsi naik pada interval .

Fungsi naik, maka:

begin mathsize 14px style f apostrophe space left parenthesis x right parenthesis greater than 0 space 3 x squared minus 3 x greater than 0 space 3 x left parenthesis x minus 1 right parenthesis greater than 0 space x subscript 1 equals 0 space a t a u space x subscript 2 equals 1 end style

Kemudian uji nilai f'(x) pada x = -1, x = begin mathsize 14px style begin inline style 1 half end style end style, dan x = 2, sehingga diperoleh garis bilangan sebagai berikut.

begin mathsize 14px style f apostrophe space left parenthesis x right parenthesis equals 3 x left parenthesis x minus 1 right parenthesis space f apostrophe space left parenthesis negative 1 right parenthesis equals 3 left parenthesis negative 1 right parenthesis left parenthesis negative 1 minus 1 right parenthesis space f apostrophe space left parenthesis negative 1 right parenthesis equals 6 greater than 0 rightwards arrow N a i k space left parenthesis plus right parenthesis  f apostrophe space left parenthesis x right parenthesis equals 3 x left parenthesis x minus 1 right parenthesis f apostrophe open parentheses 1 half close parentheses equals 3 open parentheses 1 half close parentheses open parentheses 1 half minus 1 close parentheses f apostrophe left parenthesis negative 1 right parenthesis equals negative 3 over 4 less than 0 rightwards arrow T u r u n space left parenthesis negative right parenthesis  f apostrophe space left parenthesis x right parenthesis equals 3 x left parenthesis x minus 1 right parenthesis space f apostrophe space left parenthesis 2 right parenthesis equals 3 left parenthesis 2 right parenthesis left parenthesis 2 minus 1 right parenthesis space f apostrophe space left parenthesis 2 right parenthesis equals 6 greater than 0 rightwards arrow N a i k space left parenthesis plus right parenthesis end style

Jadi, fungsi f left parenthesis x right parenthesis equals x cubed minus 3 over 2 x squared naik pada interval x less than 0 space dan space x greater than 1 space.

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