Tentukan titik balik dari f(x) = x3 – 6x2 – 9x + 1

Pertanyaan

Tentukan titik balik dari f italic left parenthesis x italic right parenthesis italic space italic equals italic space x to the power of italic 3 italic space italic – italic space italic 6 x to the power of italic 2 italic space italic – italic space italic 9 x italic space italic plus italic space italic 1

  1. (....)

  2. (....)

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

titik balik untuk undefined ada dua, yaitu begin mathsize 14px style open parentheses 2 plus square root of 7 comma negative 33 minus 14 square root of 7 close parentheses end style dan begin mathsize 14px style open parentheses 2 minus square root of 7 comma negative 33 plus 14 square root of 7 close parentheses end style.

Pembahasan

Pembahasan

Titik balik suatu fungsi begin mathsize 14px style f end style di begin mathsize 14px style x equals c end style, berlaku jika begin mathsize 14px style f to the power of apostrophe left parenthesis c right parenthesis equals 0 end style dan begin mathsize 14px style f to the power of double apostrophe left parenthesis c right parenthesis not equal to 0 end style

Dicari terlebih dahulu turunan dari begin mathsize 14px style f open parentheses x close parentheses equals x cubed minus 6 x squared minus 9 x plus 1 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell x cubed minus 6 x squared minus 9 x plus 1 end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell 3 x squared minus 12 x minus 9 end cell row cell f to the power of double apostrophe open parentheses x close parentheses end cell equals cell 6 x minus 12 end cell end table end style

Selanjutnya

begin mathsize 14px style f to the power of apostrophe open parentheses x close parentheses equals 3 x squared minus 12 x minus 9 equals 0 end style

sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row x equals cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end cell row x equals cell fraction numerator negative open parentheses negative 12 close parentheses plus-or-minus square root of open parentheses negative 12 close parentheses squared minus 4 open parentheses 3 close parentheses open parentheses negative 9 close parentheses end root over denominator 2 open parentheses 3 close parentheses end fraction end cell row x equals cell fraction numerator 12 plus-or-minus square root of 144 plus 108 end root over denominator 6 end fraction end cell row x equals cell fraction numerator 12 plus-or-minus square root of 252 over denominator 6 end fraction end cell row x equals cell fraction numerator 12 plus-or-minus 6 square root of 7 over denominator 6 end fraction end cell row x equals cell 2 plus-or-minus square root of 7 end cell end table end style

Kemudian saat begin mathsize 14px style x equals 2 plus-or-minus square root of 7 end styleundefined sehingga syarat terpenuhi.

Substitusikan undefined ke begin mathsize 14px style y equals f open parentheses x close parentheses equals x cubed minus 6 x squared minus 9 x plus 1 end style

Untuk begin mathsize 14px style x equals 2 plus square root of 7 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell x cubed minus 6 x squared minus 9 x plus 1 end cell row cell f open parentheses 2 plus square root of 7 close parentheses end cell equals cell open parentheses 2 plus square root of 7 close parentheses cubed minus 6 open parentheses 2 plus square root of 7 close parentheses squared minus 9 open parentheses 2 plus square root of 7 close parentheses plus 1 end cell row blank equals cell negative 33 minus 14 square root of 7 end cell end table end style

Untuk begin mathsize 14px style x equals 2 minus square root of 7 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell x cubed minus 6 x squared minus 9 x plus 1 end cell row cell f open parentheses 2 minus square root of 7 close parentheses end cell equals cell open parentheses 2 minus square root of 7 close parentheses cubed minus 6 open parentheses 2 minus square root of 7 close parentheses squared minus 9 open parentheses 2 minus square root of 7 close parentheses plus 1 end cell row blank equals cell negative 33 plus 14 square root of 7 end cell end table end style

Jadi titik balik untuk undefined ada dua, yaitu begin mathsize 14px style open parentheses 2 plus square root of 7 comma negative 33 minus 14 square root of 7 close parentheses end style dan begin mathsize 14px style open parentheses 2 minus square root of 7 comma negative 33 plus 14 square root of 7 close parentheses end style.

148

4.8 (12 rating)

Dani Setiyolestari

Pembahasan tidak menjabwab soal

Dhaniar Andhara

Pembahasan lengkap banget Ini yang aku cari! Bantu banget Mudah dimengerti Makasih ❤️

Ade Rahmad

wawww

Nabila Putri

Ini yang aku cari!

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Tentukan titik balik dari f(x) = −21​x2+32​x−43​

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