Roboguru

Gambarlah sketsa grafik fungsi !

Gambarlah sketsa grafik fungsi f left parenthesis x right parenthesis equals x left parenthesis x plus 3 right parenthesis left parenthesis x minus 4 right parenthesis!

Jawaban:

  • Menentukan titik potong pada sumbu-sumbu

        Titik potong sumbu X, subtitusi y equals 0

y equals 0 rightwards arrow x left parenthesis x plus 3 right parenthesis left parenthesis x minus 4 right parenthesis equals 0 x equals 0 space logical or space x equals negative 3 space logical or space x equals 4

         Sehingga titik potong sumbu X adalah left parenthesis 0 comma 0 right parenthesis comma space left parenthesis negative 3 comma 0 right parenthesis comma space dan space left parenthesis 4 comma 0 right parenthesis.

        Titik potong sumbu Y, subtitusi x equals 0

         table attributes columnalign right center left columnspacing 0px end attributes row cell 0 left parenthesis 0 plus 3 right parenthesis left parenthesis 0 minus 4 right parenthesis end cell equals y row cell left parenthesis 0 right parenthesis left parenthesis 3 right parenthesis left parenthesis negative 4 right parenthesis end cell equals y row y equals 0 end table

        Sehingga titik potong sumbu Y adalah left parenthesis 0 comma 0 right parenthesis.

  • Menentukan titik stasioner 

       Fungsi: y equals x left parenthesis x plus 3 right parenthesis left parenthesis x minus 4 right parenthesis

f apostrophe left parenthesis x right parenthesis equals 3 x squared minus 2 x minus 12 space space dan space f double apostrophe left parenthesis x right parenthesis equals 6 x minus 2

  • Syarat stasioner: f apostrophe left parenthesis x right parenthesis equals 0

space space space space space space space space space space space space space f apostrophe left parenthesis x right parenthesis equals 0 3 x squared minus 2 x minus 12 equals 0 x subscript 1 equals fraction numerator 1 minus square root of 37 over denominator 3 end fraction comma space x subscript 2 equals fraction numerator 1 plus square root of 37 over denominator 3 end fraction

  • Nilai stasionernya, subtitusi ke fungsi awal:

Untuk x equals fraction numerator 1 minus square root of 37 over denominator 3 end fraction, nilai staisonernya:

 table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses fraction numerator 1 minus square root of 37 over denominator 3 end fraction close parentheses end cell equals cell open parentheses fraction numerator 1 minus square root of 37 over denominator 3 end fraction close parentheses open parentheses fraction numerator 1 minus square root of 37 over denominator 3 end fraction plus 3 close parentheses open parentheses fraction numerator 1 minus square root of 37 over denominator 3 end fraction minus 4 close parentheses end cell row blank equals cell fraction numerator negative 110 plus 74 square root of 37 over denominator 27 end fraction end cell end table

Titik stasionernya adalah open parentheses fraction numerator 1 plus square root of 37 over denominator 3 end fraction comma fraction numerator negative 110 plus 74 square root of 37 over denominator 27 end fraction close parentheses.

Untuk x equals fraction numerator 1 plus square root of 37 over denominator 3 end fraction, nilai stasionernya:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses fraction numerator 1 plus square root of 37 over denominator 3 end fraction close parentheses end cell equals cell open parentheses fraction numerator 1 plus square root of 37 over denominator 3 end fraction close parentheses open parentheses fraction numerator 1 plus square root of 37 over denominator 3 end fraction plus 3 close parentheses open parentheses fraction numerator 1 plus square root of 37 over denominator 3 end fraction minus 4 close parentheses end cell row blank equals cell negative fraction numerator 110 plus 74 square root of 37 over denominator 27 end fraction end cell end table

 Titik stasionernya adalah open parentheses fraction numerator 1 plus square root of 37 over denominator 3 end fraction comma negative fraction numerator 110 plus 74 square root of 37 over denominator 27 end fraction close parentheses

  • Menentukan jenis stasionernya: Menggunakan turunan kedua yaitu f double apostrophe left parenthesis x right parenthesis equals 0.

begin mathsize 12px style Untuk space x equals fraction numerator 1 minus square root of 37 over denominator 3 end fraction rightwards arrow f double apostrophe left parenthesis fraction numerator 1 minus square root of 37 over denominator 3 end fraction right parenthesis equals 6 open parentheses fraction numerator 1 minus square root of 37 over denominator 3 end fraction close parentheses minus 2 equals negative 2 square root of 37 end style, jenisnya minimum. 

begin mathsize 12px style Untuk space x equals fraction numerator 1 plus square root of 37 over denominator 3 end fraction rightwards arrow f double apostrophe left parenthesis fraction numerator 1 plus square root of 37 over denominator 3 end fraction right parenthesis equals 6 open parentheses fraction numerator 1 plus square root of 37 over denominator 3 end fraction close parentheses minus 2 equals 2 square root of 37 end style, jenisnya maksimum.

Artinya titik balik minimumnya adalah open parentheses fraction numerator 1 minus square root of 37 over denominator 3 end fraction comma negative 2 square root of 37 close parentheses dan titik balik maksimumnya adalah open parentheses fraction numerator 1 plus square root of 37 over denominator 3 end fraction comma 2 square root of 37 close parentheses.

Untuk itu berikut sketsa grafiknya:

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