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Nilai maksimum dari fungsi y=31​x3+21​x2−6x+23​ adalah ...

Pertanyaan

Nilai maksimum dari fungsi y equals 1 third x cubed plus 1 half x squared minus 6 x plus 3 over 2 adalah ...

  1. 35 over 3 

  2. negative 35 over 3 

  3. 30 

  4. negative 15 

  5. 15 

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Diketahui fungsi y equals 1 third x cubed plus 1 half x squared minus 6 x plus 3 over 2.

Ingat bahwa untuk menentukan nilai maksimum dari fungsi y equals f left parenthesis x right parenthesis syaratnya yaitu f apostrophe left parenthesis x right parenthesis equals 0 dan ingat juga konsep turunan.

Titik kritis fungsi y equals 1 third x cubed plus 1 half x squared minus 6 x plus 3 over 2 yaitu 

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 1 third x cubed plus 1 half x squared minus 6 x plus 3 over 2 end cell row cell y apostrophe end cell equals cell 3 times 1 third x to the power of 3 minus 1 end exponent plus 2 times 1 half x to the power of 2 minus 1 end exponent minus 6 x to the power of 1 minus 1 end exponent plus 0 end cell row cell y apostrophe end cell equals cell 3 times 1 third x squared plus 2 times 1 half x minus 6 x to the power of 0 end cell row cell y apostrophe end cell equals cell 3 over 3 x squared plus 2 over 2 x minus 6 times 1 end cell row cell y apostrophe end cell equals cell x squared plus x minus 6 end cell row 0 equals cell x squared plus x minus 6 end cell row 0 equals cell open parentheses x plus 3 close parentheses open parentheses x minus 2 close parentheses end cell row cell x plus 3 end cell equals cell 0 space atau space straight x minus 2 equals 0 end cell row x equals cell negative 3 space atau space x equals 2 end cell end table

Titik kritisnya adalah negative 3 space atau space 2.

Nilai maksimum fungsi y equals 1 third x cubed plus 1 half x squared minus 6 x plus 3 over 2 dapat ditentukan dengan substitusi titik kritisnya ke dalam fungsi tersebut sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 1 third x cubed plus 1 half x squared minus 6 x plus 3 over 2 end cell row cell f open parentheses negative 3 close parentheses end cell equals cell 1 third open parentheses negative 3 close parentheses cubed plus 1 half open parentheses negative 3 close parentheses squared minus 6 open parentheses negative 3 close parentheses plus 3 over 2 end cell row blank equals cell 1 third open parentheses negative 27 close parentheses plus 1 half open parentheses 9 close parentheses plus 18 plus 3 over 2 end cell row blank equals cell negative 9 plus 9 over 2 plus 18 plus 3 over 2 end cell row blank equals cell fraction numerator negative 18 plus 9 plus 36 plus 3 over denominator 2 end fraction end cell row blank equals cell 30 over 2 end cell row blank equals 15 row cell f open parentheses 2 close parentheses end cell equals cell 1 third open parentheses 2 close parentheses cubed plus 1 half open parentheses 2 close parentheses squared minus 6 open parentheses 2 close parentheses plus 3 over 2 end cell row blank equals cell 1 third open parentheses 8 close parentheses plus 1 half open parentheses 4 close parentheses minus 12 plus 3 over 2 end cell row blank equals cell 8 over 3 plus 2 minus 12 plus 3 over 2 end cell row blank equals cell fraction numerator 16 plus 12 minus 72 plus 9 over denominator 6 end fraction end cell row blank equals cell 35 over 6 end cell end table 

Sehingga, nilai maksimum dari fungsi  y equals 1 third x cubed plus 1 half x squared minus 6 x plus 3 over 2 adalah 15 di titik x equals negative 3.

Jadi, jawaban yang tepat adalah E.

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