Pertanyaan

Diketahui: f ( x ) = 4 x − x 4 − 3 x x 4 + 4 . Nilai dari f ( 1 ) = …

Diketahui: $f (x) = 4 x - \frac{4}{x} - \frac{4}{3 x x} + 4$ . Nilai dari $f (1) = \dots$

L. Sibuea

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Dengan menggunakan aturan turunan fungsi aljabar, maka dari adalah Sehingga, nilai dari adalah Jadi, nilai dari adalah Oleh karena itu, jawaban yang benar adalah A.

Dengan menggunakan aturan turunan fungsi aljabar, maka f apostrophe open parentheses x close parentheses dari $f open parentheses x close parentheses equals 4 square root of x minus fraction numerator 4 over denominator square root of x end fraction minus fraction numerator 4 over denominator 3 x square root of x end fraction plus 4$ adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 4 square root of x minus fraction numerator 4 over denominator square root of x end fraction minus fraction numerator 4 over denominator 3 x square root of x end fraction plus 4 space rightwards arrow f apostrophe open parentheses x close parentheses equals n times x to the power of n minus 1 end exponent end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses 4 square root of x minus fraction numerator 4 over denominator square root of x end fraction minus fraction numerator 4 over denominator 3 x square root of x end fraction plus 4 close parentheses end cell row blank equals cell 4 times fraction numerator d over denominator d x end fraction open parentheses square root of x minus fraction numerator 1 over denominator square root of x end fraction minus fraction numerator 1 over denominator 3 x square root of x end fraction plus 1 close parentheses end cell row blank equals cell 4 times fraction numerator d over denominator d x end fraction open parentheses x to the power of 1 half end exponent close parentheses minus 4 times fraction numerator d over denominator d x end fraction open parentheses x to the power of negative 1 half end exponent close parentheses minus 4 over 3 times fraction numerator d over denominator d x end fraction open parentheses x to the power of negative 3 over 2 end exponent close parentheses plus fraction numerator d over denominator d x end fraction open parentheses 4 close parentheses end cell row blank equals cell 4 times 1 half x to the power of negative 1 half end exponent plus 4 times 1 half x to the power of negative 3 over 2 end exponent plus 4 over 3 times 3 over 2 x to the power of negative 5 over 2 end exponent plus 0 end cell row blank equals cell fraction numerator 2 over denominator square root of x end fraction plus 2 over x to the power of begin display style 3 over 2 end style end exponent plus 2 over x to the power of begin display style 5 over 2 end style end exponent end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 2 over denominator square root of x end fraction plus fraction numerator 2 over denominator x square root of x end fraction plus fraction numerator 2 over denominator x squared square root of x end fraction end cell end table$

Sehingga, nilai dari f apostrophe open parentheses 1 close parentheses adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 2 over denominator square root of x end fraction plus fraction numerator 2 over denominator x square root of x end fraction plus fraction numerator 2 over denominator x squared square root of x end fraction end cell row cell f apostrophe open parentheses 1 close parentheses end cell equals cell fraction numerator 2 over denominator square root of 1 end fraction plus fraction numerator 2 over denominator 1 square root of 1 end fraction plus fraction numerator 2 over denominator 1 squared square root of 1 end fraction end cell row cell f apostrophe open parentheses 1 close parentheses end cell equals cell 2 plus 2 plus 2 end cell row cell f apostrophe open parentheses 1 close parentheses end cell equals 6 end table$

Jadi, nilai dari f apostrophe open parentheses 1 close parentheses adalah

Oleh karena itu, jawaban yang benar adalah A.