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Fungsi  naik pada interval ....

Pertanyaan

Fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals left parenthesis x minus 2 right parenthesis left parenthesis x squared minus 4 x plus 1 right parenthesis end style naik pada interval ....

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Pembahasan Video:

Pembahasan Soal:

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals left parenthesis x minus 2 right parenthesis left parenthesis x squared minus 4 x plus 1 right parenthesis end style. Misalkan:

begin mathsize 14px style g left parenthesis x right parenthesis equals x minus 2 space space space space space space space space space space space rightwards arrow space g apostrophe left parenthesis x right parenthesis equals 1 h left parenthesis x right parenthesis equals x squared minus 4 x plus 1 space rightwards arrow space h apostrophe left parenthesis x right parenthesis equals 2 x minus 4 end style 

Turunan pertama dari fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell g apostrophe left parenthesis x right parenthesis times h left parenthesis x right parenthesis plus g left parenthesis x right parenthesis times h apostrophe left parenthesis x right parenthesis end cell row blank equals cell 1 times open parentheses x squared minus 4 x plus 1 close parentheses plus left parenthesis x minus 2 right parenthesis left parenthesis 2 x minus 4 right parenthesis end cell row blank equals cell x squared minus 4 x plus 1 plus 2 x squared minus 4 x minus 4 x plus 8 end cell row blank equals cell 3 x squared minus 12 x plus 9 end cell end table end style 

Syarat fungsi naik adalah begin mathsize 14px style f apostrophe left parenthesis x right parenthesis greater than 0 end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell greater than 0 row cell 3 x squared minus 12 x plus 9 end cell greater than 0 row cell x squared minus 4 x plus 3 end cell greater than 0 row blank blank blank end table end style

Diperoleh pembuat nol sebagai berikut.

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x minus 1 right parenthesis left parenthesis x minus 3 right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table end style 

begin mathsize 14px style x equals 1 space text atau end text space x equals 3 end style


Ambil titik pada interval begin mathsize 14px style x less than 1 end style, misal begin mathsize 14px style x equals 0 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 4 x plus 3 end cell equals cell left parenthesis 0 right parenthesis squared minus 4 left parenthesis 0 right parenthesis plus 3 end cell row blank equals 3 end table end style

Diperoleh nilai positif, artinya daerah pada interval begin mathsize 14px style x less than 1 end style bernilai positif.


Kemudian, ambil titik pada interval begin mathsize 14px style 1 less or equal than x less or equal than 3 end style, misal begin mathsize 14px style x equals 2 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 4 x plus 3 end cell equals cell left parenthesis 2 right parenthesis squared minus 4 left parenthesis 2 right parenthesis plus 3 end cell row blank equals cell negative 1 end cell end table end style

Diperoleh nilai negatif, artinya daerah pada interval begin mathsize 14px style 1 less or equal than x less or equal than 3 end style bernilai negatif.


Selanjutnya, ambil titik pada interval begin mathsize 14px style x greater than 3 end style, misal begin mathsize 14px style x equals 4 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 4 x plus 3 end cell equals cell left parenthesis 4 right parenthesis squared minus 4 left parenthesis 4 right parenthesis plus 3 end cell row blank equals 3 end table end style

Diperoleh nilai positif, artinya daerah pada interval begin mathsize 14px style x greater than 3 end style bernilai positif.

 

Jadi, fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals left parenthesis x minus 2 right parenthesis left parenthesis x squared minus 4 x plus 1 right parenthesis end style naik pada interval begin mathsize 14px style x less than 1 space text atau end text space x greater than 3 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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