Roboguru

Nilai maksimum fungsi  untuk interval  adalah ....

Nilai maksimum fungsi begin mathsize 14px style f open parentheses x close parentheses equals x cubed minus 9 x squared plus 24 x minus 18 end style untuk interval size 14px 0 size 14px less or equal than size 14px x size 14px less or equal than size 14px 5 adalah ....

  1. size 14px 25 

  2. size 14px 10 

  3. size 14px 2 

  4. size 14px minus size 14px 5 

  5. size 14px minus size 14px 18 

Jawaban:

begin mathsize 14px style f left parenthesis x right parenthesis equals x cubed minus 9 x squared plus 24 x minus 18 f apostrophe left parenthesis x right parenthesis equals 3 x squared minus 18 x plus 24 end style

Titikk Stasionernya

 begin mathsize 14px style 3 x squared minus 18 x plus 24 equals 0 left parenthesis 3 x minus 6 right parenthesis left parenthesis x minus 4 right parenthesis equals 0 x equals 2 space atau space x equals 4 end style

ambil begin mathsize 14px style x equals 0 space end styleuntuk begin mathsize 14px style x less than 2 space end style
 begin mathsize 14px style straight f apostrophe left parenthesis 0 right parenthesis equals 0 minus 0 plus 24 equals 24 blank left parenthesis greater than 0 right parenthesis end style

ambil begin mathsize 14px style x equals 3 end style untuk begin mathsize 14px style 2 less than x less than 4 end style  

begin mathsize 14px style straight f apostrophe left parenthesis 3 right parenthesis equals 3 left parenthesis 3 right parenthesis squared minus 18 left parenthesis 3 right parenthesis plus 24 equals negative 3 space left parenthesis less than 0 right parenthesis end style
ambill begin mathsize 14px style x equals 5 space end style untuk begin mathsize 14px style x greater than 4 space end style
begin mathsize 14px style straight f apostrophe left parenthesis 5 right parenthesis equals 3 left parenthesis 5 right parenthesis squared minus 18 left parenthesis 5 right parenthesis plus 24 equals 9 space left parenthesis greater than 0 right parenthesis end style 

berdasarkan gambar dapat diketahui nilai begin mathsize 14px style f apostrophe open parentheses x close parentheses end style mengalami maksimum lokal di begin mathsize 14px style x equals 2 end style 

begin mathsize 14px style f open parentheses 0 close parentheses equals 0 minus 0 plus 0 minus 18 equals negative 18 f open parentheses 2 close parentheses equals 2 cubed minus 9 open parentheses 2 close parentheses squared plus 24 open parentheses 2 close parentheses minus 18 equals 2 space open parentheses maksimum close parentheses f open parentheses 4 close parentheses equals 4 cubed minus 9 open parentheses 4 close parentheses squared plus 24 open parentheses 4 close parentheses minus 18 equals negative 2 f open parentheses 5 close parentheses equals 5 cubed minus 9 open parentheses 5 close parentheses squared plus 24 open parentheses 5 close parentheses minus 18 space equals 2 open parentheses maksimum close parentheses end style

Jadi, jawaban yang tepat adalah C 

 

0

Ruangguru

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved