Pertanyaan

Fungsi g ( x ) = sin ( x − 2 π ) + cos ( x − 2 π ) didefinisikan pada interval 0 < x < 2 π . Tentukan : b. interval fungsi g naik;

Fungsi $g (x) = sin (x - \frac{π}{2}) + cos (x - \frac{π}{2})$ didefinisikan pada interval $0 < x < 2 π$ . Tentukan :

b. interval fungsi $g$ naik;

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

naik pada interval dan .

g left parenthesis x right parenthesis equals sin open parentheses x minus straight pi over 2 close parentheses plus cos open parentheses x minus straight pi over 2 close parentheses

naik pada interval $0 less than x less than fraction numerator 3 straight pi over denominator 4 end fraction$ dan $fraction numerator 7 straight pi over denominator 4 end fraction less than x less than 2 straight pi$ .

Pembahasan

Cari turunan pertama dari . Maka Syarat Stasioner, Di dapatkan titik stasionernya adalah dan . Fungsi naik saat . Uji titik, Jadi, naik pada interval dan .

Cari turunan pertama dari g left parenthesis x right parenthesis equals sin open parentheses x minus straight pi over 2 close parentheses plus cos open parentheses x minus straight pi over 2 close parentheses . Maka

g apostrophe left parenthesis x right parenthesis equals open parentheses cos open parentheses x minus straight pi over 2 close parentheses minus sin open parentheses x minus straight pi over 2 close parentheses close parentheses

Syarat Stasioner,

$table attributes columnalign right center left columnspacing 0px end attributes row cell g apostrophe left parenthesis x right parenthesis end cell equals 0 row cell open parentheses cos open parentheses x minus straight pi over 2 close parentheses minus sin open parentheses x minus straight pi over 2 close parentheses close parentheses end cell equals 0 row cell cos open parentheses x minus straight pi over 2 close parentheses end cell equals cell sin open parentheses x minus straight pi over 2 close parentheses end cell row cell fraction numerator sin open parentheses x minus straight pi over 2 close parentheses over denominator cos open parentheses x minus straight pi over 2 close parentheses end fraction end cell equals 1 row cell tan open parentheses x minus straight pi over 2 close parentheses end cell equals 1 row cell ta n open parentheses x minus straight pi over 2 close parentheses end cell equals cell tan straight pi over 4 end cell row cell x minus straight pi over 2 end cell equals cell straight pi over 4 plus k straight pi end cell row straight x equals cell straight pi over 4 plus straight pi over 2 plus kπ end cell row straight x equals cell straight pi over 4 plus fraction numerator 2 straight pi over denominator 4 end fraction plus kπ end cell row straight x equals cell fraction numerator 3 straight pi over denominator 4 end fraction plus kπ end cell row straight k equals 0 row straight x equals cell fraction numerator 3 straight pi over denominator 4 end fraction plus 0 times straight pi end cell row straight x equals cell fraction numerator 3 straight pi over denominator 4 end fraction end cell row straight k equals 1 row straight x equals cell fraction numerator 3 straight pi over denominator 4 end fraction plus 1 times straight pi end cell row straight x equals cell fraction numerator 7 straight pi over denominator 4 end fraction end cell row blank blank blank end table$

Di dapatkan titik stasionernya adalah $x equals fraction numerator 3 straight pi over denominator 4 end fraction$ dan $x equals fraction numerator 7 straight pi over denominator 4 end fraction$ .

Fungsi naik saat g apostrophe left parenthesis x right parenthesis greater than 0 .

Uji titik,

Jadi, g left parenthesis x right parenthesis equals sin open parentheses x minus straight pi over 2 close parentheses plus cos open parentheses x minus straight pi over 2 close parentheses naik pada interval $0 less than x less than fraction numerator 3 straight pi over denominator 4 end fraction$ dan $fraction numerator 7 straight pi over denominator 4 end fraction less than x less than 2 straight pi$ .