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Tentukan titik stasioner dari fungsi  !

Pertanyaan

Tentukan titik stasioner dari fungsi straight F left parenthesis x right parenthesis equals x cubed minus 6 x squared plus 3 x minus 8 !

Pembahasan Soal:

Titik stasioner dapat dicari menggunakan konsep turunan pertama

Diketahui fungsi straight F left parenthesis x right parenthesis equals x cubed minus 6 x squared plus 3 x minus 8.

table attributes columnalign right center left columnspacing 0px end attributes row cell straight F apostrophe left parenthesis straight x right parenthesis end cell equals 0 row cell 3 x squared minus 12 x plus 3 end cell equals 0 row cell x squared minus 4 x plus 1 end cell equals 0 end table 

Untuk mencari akar-akarnya digunakan rumus ABC:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight x subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative straight b plus-or-minus square root of straight b squared minus 4 ac end root over denominator 2 straight a end fraction end cell row blank equals cell fraction numerator 4 plus-or-minus square root of 16 minus 4 end root over denominator 2 end fraction end cell row blank equals cell fraction numerator 4 plus-or-minus square root of 12 over denominator 2 end fraction end cell row blank equals cell fraction numerator 4 plus-or-minus 2 square root of 3 over denominator 2 end fraction end cell row blank equals cell 2 plus-or-minus square root of 3 end cell end table  

Lalu akan di hitung nilai stasioner untuk masing-masing x sebagai berikut.

Untuk x subscript 1 equals 2 plus square root of 3, nilai stasionernya adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell straight F left parenthesis 2 plus square root of 3 right parenthesis end cell equals cell open parentheses 2 plus square root of 3 close parentheses cubed minus 6 open parentheses 2 plus square root of 3 close parentheses squared plus 3 open parentheses 2 plus square root of 3 close parentheses minus 8 end cell row blank equals cell 2 cubed plus 3 times thin space 2 squared square root of 3 plus 3 times thin space 2 open parentheses square root of 3 close parentheses squared plus open parentheses square root of 3 close parentheses cubed minus 6 open parentheses 2 squared plus 2 times thin space 2 square root of 3 plus open parentheses square root of 3 close parentheses squared close parentheses plus 6 plus 3 square root of 3 minus 8 end cell row blank equals cell 8 plus 12 square root of 3 plus 18 plus 3 square root of 3 minus 24 minus 24 square root of 3 minus 18 plus 6 plus 3 square root of 3 minus 8 end cell row blank equals cell 26 plus 15 square root of 3 minus 42 minus 24 square root of 3 minus 2 plus 3 square root of 3 end cell row blank equals cell negative 18 minus 6 square root of 3 end cell end table 
 

Untuk x subscript 2 equals 2 minus square root of 3, nilai stasionernya adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell straight F left parenthesis 2 minus square root of 3 right parenthesis end cell equals cell open parentheses 2 minus square root of 3 close parentheses cubed minus 6 open parentheses 2 minus square root of 3 close parentheses squared plus 3 open parentheses 2 minus square root of 3 close parentheses minus 8 end cell row blank equals cell 2 cubed minus 3 times thin space 2 squared square root of 3 plus 3 times thin space 2 open parentheses square root of 3 close parentheses squared minus open parentheses square root of 3 close parentheses cubed minus 6 open parentheses 2 squared minus 2 times thin space 2 square root of 3 plus open parentheses square root of 3 close parentheses squared close parentheses plus 6 minus 3 square root of 3 minus 8 end cell row blank equals cell 8 minus 12 square root of 3 plus 18 minus 3 square root of 3 minus 24 plus 24 square root of 3 minus 18 plus 6 minus 3 square root of 3 minus 8 end cell row blank equals cell 26 minus 15 square root of 3 minus 42 plus 24 square root of 3 minus 2 minus 3 square root of 3 end cell row blank equals cell negative 18 plus 6 square root of 3 end cell end table 
 

Jadi, titik stasioner dari fungsi straight F left parenthesis x right parenthesis equals x cubed minus 6 x squared plus 3 x minus 8 adalah open parentheses 2 plus square root of 3 comma space minus 18 minus 6 square root of 3 close parentheses dan open parentheses 2 minus square root of 3 comma space minus 18 plus 6 square root of 3 close parentheses.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 27 April 2021

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