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Nilai maksimum fungsi untuk interval adalah…

Nilai maksimum fungsi begin mathsize 14px style f open parentheses x close parentheses equals x cubed minus 9 x squared plus 15 x end style untuk interval begin mathsize 14px style negative 1 less or equal than x less or equal than 7 end style adalah…

Jawaban:

Nilai maksimum suatu fungsi dalam interval tertutup adalah nilai terbesar dalam suatu fungsi dan menggunakan tanda ketaksamaan undefined.

Langkah mencari nilai maksimum suatu fungsi:

Tentukan nilai stasioner

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 x cubed minus 9 x squared plus 15 x end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 3 x squared minus 18 x plus 15 end cell row blank equals cell x squared minus 6 x plus 5 end cell end table end style

Ubah menjadi begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals 0 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 6 x plus 5 end cell equals 0 row cell left parenthesis x minus 1 right parenthesis left parenthesis x minus 5 right parenthesis end cell equals 0 end table end style 

Sehingga diperoleh begin mathsize 14px style x equals 1 comma space x equals 5 end style

Menentukan batas bawah dan batas atas interval undefined

Batas bawah begin mathsize 14px style f left parenthesis a right parenthesis equals f left parenthesis negative 1 right parenthesis end style

Batas atas begin mathsize 14px style f left parenthesis b right parenthesis equals f left parenthesis 7 right parenthesis end style

Menentukan nilai maksimum

Untuk begin mathsize 14px style x equals 1 end style, maka:

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 x cubed minus 9 x squared plus 15 x end cell row cell f left parenthesis 1 right parenthesis end cell equals cell left parenthesis 1 right parenthesis cubed minus 9 left parenthesis 1 right parenthesis squared plus 15 left parenthesis 1 right parenthesis end cell row blank equals cell 1 minus 9 plus 15 end cell row blank equals 7 end table end style

Untuk begin mathsize 14px style x equals 5 end style, maka:

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 x cubed minus 9 x squared plus 15 x end cell row cell f left parenthesis 5 right parenthesis end cell equals cell left parenthesis 5 right parenthesis cubed minus 9 left parenthesis 5 right parenthesis squared plus 15 left parenthesis 5 right parenthesis end cell row blank equals cell 125 minus 225 plus 75 end cell row blank equals cell negative 25 end cell end table end style

Untuk begin mathsize 14px style x equals negative 1 end style, maka:

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 x cubed minus 9 x squared plus 15 x end cell row cell f left parenthesis negative 1 right parenthesis end cell equals cell 〖 left parenthesis negative 1 right parenthesis 〗 cubed minus 9 〖 left parenthesis negative 1 right parenthesis 〗 squared plus 15 left parenthesis negative 1 right parenthesis end cell row blank equals cell negative 1 minus 9 minus 15 end cell row blank equals cell negative 25 end cell end table end style

Untuk begin mathsize 14px style x equals 7 end style, maka:

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 x cubed minus 9 x squared plus 15 x end cell row blank equals cell left parenthesis 7 right parenthesis cubed minus 9 left parenthesis 7 right parenthesis squared plus 15 left parenthesis 7 right parenthesis end cell row blank equals cell 343 minus 441 plus 105 end cell row blank equals 7 end table end style 

Jadi, nilai maksimum fungsi undefined untuk interval undefined adalah begin mathsize 14px style 7 end style.

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