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Diketahui fungsi f ditentukan dengan rumus f(x)=x+x1​, x=0, x∈R.  a. Carilah turunan pertama dari fungsi, kemudian tentukan nilai-nilai stasionenya.

Pertanyaan

Diketahui fungsi f ditentukan dengan rumus f left parenthesis x right parenthesis equals x plus 1 over x comma space x not equal to 0 comma space x element of R. 

a. Carilah turunan pertama dari fungsi, kemudian tentukan nilai-nilai stasionenya.

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

Titik-titk sationernya left parenthesis x comma space f left parenthesis x right parenthesis right parenthesis adalah left parenthesis negative 1 comma space minus 2 right parenthesis dan left parenthesis 1 comma space 2 right parenthesis

Pembahasan

Turunan fungsi aljabar.

straight f left parenthesis straight x right parenthesis equals ax to the power of straight n space rightwards arrow straight f apostrophe left parenthesis straight x right parenthesis equals nax to the power of straight n minus 1 end exponent 

Maka :

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 x plus 1 over straight x end cell row cell straight f left parenthesis straight x right parenthesis end cell equals cell straight x plus straight x to the power of negative 1 end exponent end cell row cell straight f apostrophe left parenthesis straight x right parenthesis end cell equals cell straight x to the power of 1 minus 1 end exponent plus left parenthesis negative 1 right parenthesis straight x to the power of negative 1 minus 1 end exponent end cell row blank equals cell 1 minus straight x to the power of negative 2 end exponent end cell end table 

Titik stasioner jika straight f apostrophe left parenthesis straight x right parenthesis equals 0 maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight f apostrophe left parenthesis straight x right parenthesis end cell equals cell 1 minus straight x to the power of negative 2 end exponent end cell row 0 equals cell 1 minus straight x to the power of negative 2 end exponent end cell row cell straight x to the power of negative 2 end exponent end cell equals 1 row cell 1 over straight x squared end cell equals 1 row cell straight x squared end cell equals 1 row straight x equals cell plus-or-minus square root of 1 end cell row blank equals cell plus-or-minus 1 end cell end table 

Untuk straight x equals 1 maka :

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 x plus 1 over straight x end cell row cell straight f left parenthesis 1 right parenthesis end cell equals cell 1 plus 1 over 1 end cell row blank equals 2 end table  

Untuk x equals negative 1 maka :

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 x plus 1 over straight x end cell row cell straight f left parenthesis negative 1 right parenthesis end cell equals cell negative 1 plus fraction numerator 1 over denominator negative 1 end fraction end cell row blank equals cell negative 1 minus 1 end cell row blank equals cell negative 2 end cell end table 

Jadi, Titik-titk sationernya left parenthesis x comma space f left parenthesis x right parenthesis right parenthesis adalah left parenthesis negative 1 comma space minus 2 right parenthesis dan left parenthesis 1 comma space 2 right parenthesis

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