Analisis dan sketsa kurva fungsi f(x)=x4+2x3.

Pertanyaan

Analisis dan sketsa kurva fungsi 

  1. ...

  2. ...

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Pembahasan

Analisis kurva begin mathsize 14px style f open parentheses x close parentheses equals x to the power of 4 plus 2 x cubed end style

Menentukan titik potong sumbu begin mathsize 14px style x end stylebegin mathsize 14px style y equals 0 end style

begin mathsize 14px style x to the power of 4 plus 2 x cubed equals 0 x cubed open parentheses x plus 2 close parentheses equals 0 x equals 0 comma space x equals negative 2 end style 

Jadi titik potong sumbu undefined ada pada titik begin mathsize 14px style left parenthesis 0 comma 0 right parenthesis end style dan begin mathsize 14px style left parenthesis negative 2 comma 0 right parenthesis end style.

Menentukan titik potong sumbu begin mathsize 14px style y end stylebegin mathsize 14px style x equals 0 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 to the power of 4 plus 2 x cubed end cell row cell f open parentheses 0 close parentheses end cell equals cell open parentheses 0 close parentheses to the power of 4 plus 2 open parentheses 0 close parentheses cubed end cell row blank equals 0 end table end style

Jadi titik potong sumbu undefined ada pada titik undefined.

Menentukan titik stasioner, begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals 0 end style

begin mathsize 14px style f to the power of apostrophe open parentheses x close parentheses equals 4 x cubed plus 6 x squared equals 0 2 x squared open parentheses 2 x plus 3 close parentheses equals 0 x equals 0 comma x equals negative 3 over 2 end style

Untuk undefined

undefined

Untuk begin mathsize 14px style x equals negative 3 over 2 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 to the power of 4 plus 2 x cubed end cell row cell f open parentheses negative 3 over 2 close parentheses end cell equals cell open parentheses negative 3 over 2 close parentheses to the power of 4 plus 2 open parentheses negative 3 over 2 close parentheses cubed end cell row blank equals cell 81 over 16 plus 2 open parentheses negative 27 over 8 close parentheses end cell row blank equals cell fraction numerator 81 minus 108 over denominator 16 end fraction end cell row blank equals cell negative 27 over 16 end cell end table end style

Jadi titik stasioner ada pada titik undefined dan begin mathsize 14px style open parentheses negative 3 over 2 comma negative 27 over 16 close parentheses end style.

Menentukan interval naik dan turun.

Batas-batas, begin mathsize 14px style x equals 0 end style dan begin mathsize 14px style x equals negative 3 over 2 end style, untuk begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals 4 x cubed plus 6 x end style

Saat begin mathsize 14px style x less than negative 3 over 2 end stylebegin mathsize 14px style f apostrophe left parenthesis x right parenthesis less than 0 end style maka undefined adalah interval turun.

Saat begin mathsize 14px style negative 3 over 2 less than x less than 0 end style atau begin mathsize 14px style x greater than 0 end stylebegin mathsize 14px style f apostrophe left parenthesis x right parenthesis greater than 0 end style maka undefined atau undefined adalah interval naik.

Uji turunan kedua

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 to the power of 4 plus 2 x cubed end cell row cell f to the power of apostrophe open parentheses x close parentheses end cell equals cell 4 x cubed plus 6 x squared end cell row cell f to the power of apostrophe apostrophe end exponent open parentheses x close parentheses end cell equals cell 12 x squared plus 12 x end cell end table end style

Untuk undefined

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of apostrophe apostrophe end exponent open parentheses x close parentheses end cell equals cell 12 x squared plus 12 x end cell row cell f to the power of apostrophe apostrophe end exponent open parentheses 0 close parentheses end cell equals cell 12 open parentheses 0 close parentheses squared plus 12 open parentheses 0 close parentheses end cell row blank equals 0 end table end style

Karena begin mathsize 14px style f double apostrophe left parenthesis 0 right parenthesis equals 0 end style, maka titik undefined adalah titik belok.

Untuk undefined

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of apostrophe apostrophe end exponent open parentheses x close parentheses end cell equals cell 12 x squared plus 12 x end cell row cell f to the power of apostrophe apostrophe end exponent open parentheses negative 3 over 2 close parentheses end cell equals cell 12 open parentheses negative 3 over 2 close parentheses squared plus 12 open parentheses negative 3 over 2 close parentheses end cell row blank equals cell 12 open parentheses 9 over 4 close parentheses minus 18 end cell row blank equals cell 27 minus 18 end cell row blank equals 9 end table end style

Karena begin mathsize 14px style f apostrophe apostrophe open parentheses negative 3 over 2 close parentheses greater than 0 end style, maka titik begin mathsize 14px style open parentheses negative 3 over 2 comma negative 27 over 16 close parentheses end style adalah titik balik minimum.

Sketsa grafik:

299

5.0 (3 rating)

Pertanyaan serupa

Sketsa grafik f(x)=x3−3x2+4x−2 yang tepat adalah ….

55

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Fitur Roboguru

Topik Roboguru

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia