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Diketahui . Jika , fungsi  naik pada selang ....

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals 2 over 3 x cubed minus 1 half x squared minus 3 x plus 1 over 6 end style. Jika size 14px g begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px f begin mathsize 14px style left parenthesis 1 minus x right parenthesis end style, fungsi undefined naik pada selang ....

  1. size 14px minus size 14px 2 size 14px less than size 14px x size 14px less than size 14px 1 over size 14px 2 

  2. size 14px minus size 14px 2 size 14px less than size 14px x size 14px less than size 14px minus size 14px 1 over size 14px 2 

  3. size 14px minus size 14px 1 size 14px less than size 14px x size 14px less than size 14px 3 over size 14px 2 

  4. size 14px minus size 14px 3 over size 14px 2 size 14px less than size 14px x size 14px less than size 14px 1 

  5. size 14px minus size 14px 1 over size 14px 2 size 14px less than size 14px x size 14px less than size 14px 2 

Jawaban:

begin mathsize 14px style g open parentheses x close parentheses equals f open parentheses 1 minus x close parentheses space space space space space space equals 2 over 3 open parentheses 1 minus x close parentheses cubed minus 1 half open parentheses 1 minus x close parentheses squared minus 3 open parentheses 1 minus x close parentheses plus 1 over 6 space space space space space space equals 2 over 3 open parentheses 1 minus 3 x plus 3 x squared minus x cubed close parentheses minus 1 half open parentheses 1 minus 2 x plus x squared close parentheses minus 3 plus 3 x plus 1 over 6 space space space space space space equals 2 over 3 minus 2 x plus 2 x squared minus 2 over 3 x cubed minus 1 half plus x minus 1 half x squared minus 3 plus 3 x plus 1 over 6 space space space space space space equals negative 2 over 3 x cubed plus 3 over 2 x squared plus 2 x minus 8 over 3  end style 

fungsi undefined naik pada saat undefined 
begin mathsize 14px style negative 2 x squared plus 3 x plus 2 greater than 0 left parenthesis negative 2 x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis greater than 0 end style  
Pembuat nol sebagai berikut:
begin mathsize 14px style left parenthesis negative 2 x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis equals 0 x equals negative 1 half atau blank x equals 2 end style 

diagram nilai begin mathsize 14px style g apostrophe open parentheses x close parentheses end style sebagai berikut

Dari diagram di atas terlihat bahwa begin mathsize 14px style g apostrophe open parentheses x close parentheses greater than 0 end style pada interval size 14px minus size 14px 1 over size 14px 2 size 14px less than size 14px x size 14px less than size 14px 2 

Jadi, jawaban yang tepat adalah E

 

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