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Jika f(2x+4)=36x−1​,x>61​   dan f (x) menyatakan turunan pertama dari f(x), maka nilai dari 2f (4)=  ….

Pertanyaan

Jika begin mathsize 14px style straight f left parenthesis 2 straight x plus 4 right parenthesis equals cube root of 6 straight x minus 1 end root comma straight x greater than 1 over 6 end style   dan begin mathsize 14px style f to the power of apostrophe left parenthesis x right parenthesis end style menyatakan turunan pertama dari undefined, maka nilai dari begin mathsize 14px style 2 straight f to the power of apostrophe left parenthesis 4 right parenthesis equals end style  ….

  1. begin mathsize 14px style negative 2 end style

  2. begin mathsize 14px style negative 1 end style

  3. begin mathsize 14px style 0 end style

  4. begin mathsize 14px style 1 end style

  5. begin mathsize 14px style 2 end style

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawabannya adalah E.

Pembahasan

Misalkan:

begin mathsize 14px style straight y equals 2 straight x plus 4 rightwards arrow straight x equals 1 half left parenthesis straight y minus 4 right parenthesis end style 

Maka diperoleh fungsi undefined sebagai berikut.

undefined   

Sehingga,

begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals left parenthesis 3 straight x minus 13 right parenthesis to the power of 1 third end exponent end style 

Misalkan:

begin mathsize 14px style straight u equals 3 straight x minus 13 rightwards arrow straight u to the power of apostrophe equals 3 end style 

Kemudian, hitung turunan pertama undefined 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis end cell equals cell straight u to the power of 1 third end exponent end cell row cell straight f to the power of apostrophe left parenthesis straight x right parenthesis end cell equals cell 1 third straight u to the power of 1 third minus 1 end exponent times straight u to the power of apostrophe end cell row blank equals cell 1 third straight u to the power of negative 2 over 3 end exponent times 3 end cell row blank equals cell 1 over straight u to the power of begin display style 2 over 3 end style end exponent end cell row blank equals cell fraction numerator 1 over denominator cube root of left parenthesis 3 straight x minus 13 right parenthesis squared end root end fraction end cell end table end style 

Jadi, diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight f to the power of apostrophe left parenthesis 4 right parenthesis end cell equals cell 2 times fraction numerator 1 over denominator cube root of left parenthesis 3 left parenthesis 4 right parenthesis minus 13 right parenthesis squared end root end fraction end cell row blank equals cell fraction numerator 2 over denominator cube root of left parenthesis negative 1 right parenthesis squared end root end fraction end cell row blank equals cell 2 over 1 end cell row blank equals 2 end table end style 

Jadi, jawabannya adalah E.

39

3.0 (2 rating)

Pertanyaan serupa

Jika f(x)=4(2x−3)​,  x>23​ maka nilai dari 4⋅f (2x−3) adalah ….

32

0.0

Jawaban terverifikasi

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