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Diketahui f ( x ) = 5 x 4 + 7 x 3 − 4 x 3 − 4 x 2 − 2 x + 1 , tentukan f ( 3 ) = ...

Diketahui , tentukan space 

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A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

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 f apostrophe open parentheses 3 close parentheses equals 595.

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Pembahasan

Ingat! Keterangan: Fungsi di atas dapat disederhanakan menjadi: Tentukan turunan pertama fungsi . Maka, nilai dari . Jadi, .

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell a x to the power of n plus c end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell n times a x to the power of n minus 1 end exponent end cell end table 

Keterangan:

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell turunan space pertama space fungsi space f left parenthesis x right parenthesis end cell row a equals cell koefisien space variabel space x end cell row n equals cell bilangan space pangkat end cell row c equals konstanta end table 

Fungsi di atas dapat disederhanakan menjadi:

f open parentheses x close parentheses equals 5 x to the power of 4 plus 7 x cubed minus 4 x cubed minus 4 x squared minus 2 x plus 1 f open parentheses x close parentheses equals 5 x to the power of 4 plus 3 x cubed minus 4 x squared minus 2 x plus 1 

Tentukan turunan pertama fungsi f open parentheses x close parentheses.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 5 x to the power of 4 plus 3 x cubed minus 4 x squared minus 2 x plus 1 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 4 times 5 x to the power of 4 minus 1 end exponent plus 3 times 3 x to the power of 3 minus 1 end exponent minus 2 times 4 x to the power of 2 minus 1 end exponent minus 1 times 2 x to the power of 1 minus 1 end exponent plus 0 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 20 x cubed plus 9 x squared minus 8 x minus 2 end cell end table 

Maka, nilai dari f apostrophe open parentheses 3 close parentheses.

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell 20 x cubed plus 9 x squared minus 8 x minus 2 end cell row cell f apostrophe open parentheses 3 close parentheses end cell equals cell 20 times 3 cubed plus 9 times 3 squared minus 8 times 3 minus 2 end cell row blank equals cell 540 plus 81 minus 24 minus 2 end cell row blank equals 595 end table

Jadi, f apostrophe open parentheses 3 close parentheses equals 595.

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