Nilai minimum fungsi f(x)=2x3+27x2+108x+120 untuk −7≤x≤0 adalah ....

Pertanyaan

Nilai minimum fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x cubed plus 27 x squared plus 108 x plus 120 end style untuk size 14px minus size 14px 7 size 14px less or equal than size 14px x size 14px less or equal than size 14px 0 adalah ....

  1. size 14px minus size 14px 100 

  2. size 14px minus size 14px 25 

  3. size 14px minus size 14px 15 

  4. size 14px minus size 14px 5 

  5. size 14px 0 

P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x cubed plus 27 x squared plus 108 x plus 120 end style. Nilai minimum fungsi dicapai saat turunan pertama fungsi sama dengan 0, sehingga diperoleh:

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 6 x squared plus 54 x plus 108 end cell row 0 equals cell 6 x squared plus 54 x plus 108 end cell row 0 equals cell x squared plus 9 x plus 18 end cell row 0 equals cell open parentheses x plus 3 close parentheses left parenthesis x plus 6 right parenthesis end cell row x equals cell negative 3 space atau space x equals negative 6 end cell end table end style 

Karena diperoleh table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px x end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px x end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 14px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 14px 6 end table yang memenuhi interval yang diberikan pada soal yaitu begin mathsize 14px style negative 7 less or equal than x less or equal than 0 end style, maka akan disubstitusikan kedua nilai tersebut pada fungsi untuk mendapatkan nilai minimum dan titik balik minimum.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 2 x cubed plus 27 x squared plus 108 x plus 120 end cell row cell f left parenthesis negative 3 right parenthesis end cell equals cell 2 left parenthesis negative 3 right parenthesis blank cubed plus 27 left parenthesis negative 3 right parenthesis blank squared plus 108 open parentheses negative 3 close parentheses plus 120 end cell row blank equals cell 2 open parentheses negative 27 close parentheses plus 27 open parentheses 9 close parentheses plus 108 open parentheses negative 3 close parentheses plus 120 end cell row blank equals cell negative 54 plus 243 minus 324 plus 120 end cell row blank equals cell negative 15 end cell row cell f left parenthesis negative 6 right parenthesis end cell equals cell 2 left parenthesis negative 6 right parenthesis blank cubed plus 27 left parenthesis negative 6 right parenthesis blank squared plus 108 open parentheses negative 6 close parentheses plus 120 end cell row blank equals cell 2 left parenthesis negative 216 right parenthesis plus 27 left parenthesis 36 right parenthesis plus 108 left parenthesis negative 6 right parenthesis plus 120 end cell row blank equals cell negative 432 plus 972 minus 648 plus 120 end cell row blank equals 12 end table end style 

Dengan demikian, nilai minimum fungsi tersebut adalah begin mathsize 14px style negative 12 end style dengan titik balik minimum begin mathsize 14px style open parentheses negative 3 comma space minus 15 close parentheses end style.

Jadi, jawaban yang benar adalah C.

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