Pertanyaan

Periksa apakah fungsi f ( x ) = sin ( x + π ) merupakan fungsi naik atau fungsi turun pada interval-interval berikut. a. [ 2 3 π , 2 π ]

Periksa apakah fungsi $f (x) = sin (x + π)$ merupakan fungsi naik atau fungsi turun pada interval-interval berikut.

a. $[\frac{3 π}{2}, 2 π]$

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Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

pada interval fungsi merupakan fungsi turun.

pada interval $open square brackets fraction numerator 3 straight pi over denominator 2 end fraction comma 2 straight pi close square brackets$ fungsi f left parenthesis x right parenthesis equals sin open parentheses x plus straight pi close parentheses

f left parenthesis x right parenthesis equals sin open parentheses x plus straight pi close parentheses

merupakan fungsi turun.

Pembahasan

Fungsi naik apabila Fungsi turun apabila Fungsi tetap atau statis apabila Cari turunan , Interval maka , Maka . Jadi, pada interval fungsi merupakan fungsi turun.

Fungsinaik apabila
Fungsi turun apabila
Fungsi tetap atau statis apabila

Cari turunan f left parenthesis x right parenthesis equals sin open parentheses x plus straight pi close parentheses ,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses negative sin open parentheses x close parentheses close parentheses end cell equals cell negative fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x close parentheses close parentheses end cell row blank equals cell negative cos open parentheses x close parentheses end cell end table$

Interval $open square brackets fraction numerator 3 straight pi over denominator 2 end fraction comma 2 straight pi close square brackets$ maka $fraction numerator 3 straight pi over denominator 2 end fraction less than x less than straight pi over 2$ ,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 straight pi over denominator 2 end fraction end cell less than cell x less than straight pi over 2 end cell row cell fraction numerator 3 open parentheses 180 close parentheses over denominator 3 end fraction end cell less than cell x less than 180 over 2 end cell row cell 540 over 3 end cell less than cell x less than 90 end cell row 180 less than cell x less than 90 end cell row cell negative 1 end cell less than cell x less than 0 end cell end table$

Maka f left parenthesis x right parenthesis apostrophe less than 0 .

Jadi, pada interval $open square brackets fraction numerator 3 straight pi over denominator 2 end fraction comma 2 straight pi close square brackets$ fungsi f left parenthesis x right parenthesis equals sin open parentheses x plus straight pi close parentheses merupakan fungsi turun.