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Jika begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 4 x minus 1 over denominator 3 x plus 2 end fraction end style, maka begin mathsize 14px style f to the power of apostrophe open parentheses 0 close parentheses equals... end style 

  1. begin mathsize 14px style 11 over 4 end style 

  2. begin mathsize 14px style 3 end style  

  3. begin mathsize 14px style 7 over 2 end style  

  4. begin mathsize 14px style 15 over 4 end style 

  5. begin mathsize 14px style 4 end style  

Pembahasan Video:

Pembahasan Soal:

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 4 x minus 1 over denominator 3 x plus 2 end fraction end style. Misalkan,

begin mathsize 14px style g left parenthesis x right parenthesis equals 4 x minus 1 rightwards arrow g apostrophe left parenthesis x right parenthesis equals 4 h left parenthesis x right parenthesis equals 3 x plus 2 rightwards arrow h apostrophe left parenthesis x right parenthesis equals 3 end style.

Turunan pertama dari fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style adalah,

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 fraction numerator g left parenthesis x right parenthesis over denominator h left parenthesis x right parenthesis end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator g apostrophe left parenthesis x right parenthesis times h left parenthesis x right parenthesis minus g left parenthesis x right parenthesis times h apostrophe left parenthesis x right parenthesis over denominator h squared left parenthesis x right parenthesis end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 4 left parenthesis 3 x plus 2 right parenthesis minus left parenthesis 4 x minus 1 right parenthesis left parenthesis 3 right parenthesis over denominator left parenthesis 3 x plus 2 right parenthesis squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 12 x plus 8 minus 12 x plus 3 over denominator left parenthesis 3 x plus 2 right parenthesis squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 11 over left parenthesis 3 x plus 2 right parenthesis squared end cell end table end style  

Nilai dari begin mathsize 14px style f apostrophe left parenthesis 0 right parenthesis end style adalah,

begin mathsize 14px style f apostrophe left parenthesis 0 right parenthesis equals 11 over left parenthesis 3 times 0 plus 2 right parenthesis squared equals 11 over 4 end style 

Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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