Pertanyaan

Nilai balik maksimum dari f ( x ) = 2 1 2 x + cos x adalah...

Nilai balik maksimum dari $f (x) = \frac{1}{2} 2 x + cos x$ adalah...

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Habis dalam

Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Tentukan turunan pertama dari Syarat stasioner Menentukan nilai stasioner, Jadi nilai stasionernya adalah dan . pasti positif karena berada pada kuadran pertama. Oleh karena itu, jawaban yang benar adalah C.

Tentukan turunan pertama dari f left parenthesis x right parenthesis equals 1 half square root of 2 x plus cos space x

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses 1 half square root of 2 x plus cos open parentheses x close parentheses close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses fraction numerator x over denominator square root of 2 end fraction plus cos open parentheses x close parentheses close parentheses end cell row blank equals cell fraction numerator d over denominator d x end fraction open parentheses fraction numerator x over denominator square root of 2 end fraction close parentheses plus fraction numerator d over denominator d x end fraction open parentheses cos open parentheses x close parentheses close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 2 end fraction fraction numerator d over denominator d x end fraction open parentheses x close parentheses minus sin open parentheses x close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 2 end fraction times thin space 1 minus sin open parentheses x close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 2 end fraction minus sin open parentheses x close parentheses end cell row blank equals cell 1 half square root of 2 minus sin open parentheses x close parentheses end cell end table$

Syarat stasioner f apostrophe left parenthesis x right parenthesis equals 0

Menentukan nilai stasioner,

$table attributes columnalign right center left columnspacing 0px end attributes row x equals 45 row cell f left parenthesis 45 right parenthesis end cell equals cell 1 half square root of 2 open parentheses straight pi over 4 close parentheses plus cos 45 degree end cell row blank equals cell straight pi over 8 square root of 2 plus 1 half square root of 2 end cell row blank blank blank row x equals 135 row cell f left parenthesis 135 right parenthesis end cell equals cell 1 half square root of 2 open parentheses fraction numerator 3 straight pi over denominator 4 end fraction close parentheses plus cos 135 end cell row blank equals cell fraction numerator 3 straight pi over denominator 8 end fraction plus 1 half square root of 2 end cell end table$

Jadi nilai stasionernya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets straight pi over 4 comma straight pi over 8 square root of 2 plus 1 half square root of 2 close square brackets end cell end table dan $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets fraction numerator 3 straight pi over denominator 4 end fraction comma fraction numerator 3 straight pi over denominator 8 end fraction plus 1 half square root of 2 close square brackets end cell end table$ .

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open square brackets straight pi over 4 comma straight pi over 8 square root of 2 plus 1 half square root of 2 close square brackets end cell end table pasti positif karena berada pada kuadran pertama.

Oleh karena itu, jawaban yang benar adalah C.