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1. Grafik fungsi  akan naik pada interval...

Pertanyaan

1. Grafik fungsi y equals sin space 2 x akan naik pada interval...space 

  1. 0 less than x less than straight pi 

  2. 0 less than x less than 1 half straight pi 

  3. 1 half straight pi less than x less than straight pi 

  4. 3 over 4 straight pi less than x less than 1 1 fourth straight pi 

  5. straight pi less than x less than 2 straight pi 

Pembahasan Soal:

Fungsi naik terjadi pada suatu interval ketika f apostrophe open parentheses x close parentheses greater than 0. Maka kita perlu untuk menentukan titik kritisnya/titik beloknya dahulu yaitu ketika f apostrophe open parentheses x close parentheses equals 0. Untuk menyelesaikan soal di atas, perhatikan penghitungan berikut!

 y equals sin space g open parentheses x close parentheses y apostrophe equals cos space g open parentheses x close parentheses space g apostrophe open parentheses x close parentheses  y equals sin space 2 x y apostrophe equals cos space 2 x times 2 equals 2 space cos space 2 x y apostrophe greater than 0 2 space cos space 2 x greater than 0 left right arrow cos space 2 x greater than 0 x equals straight pi over 4 space logical or x equals fraction numerator 3 straight pi over denominator 4 end fraction logical or x equals fraction numerator 5 straight pi over denominator 4 end fraction 

Untuk interval 0 less than x less than straight pi over 4 

 x equals straight pi over 8 y apostrophe open parentheses x close parentheses equals 2 space cos space 2 x y apostrophe open parentheses straight pi over 8 close parentheses equals 2 space cos space open parentheses 2 open parentheses straight pi over 8 close parentheses close parentheses y apostrophe open parentheses straight pi over 8 close parentheses equals 2 space cos space open parentheses 45 degree close parentheses y apostrophe open parentheses straight pi over 8 close parentheses equals 2 space 1 half square root of 2 y apostrophe open parentheses straight pi over 8 close parentheses equals square root of 2 space greater than 0 

Untuk interval straight pi over 4 less than x less than fraction numerator 3 straight pi over denominator 4 end fraction 

 x equals straight pi over 2 y apostrophe open parentheses x close parentheses equals 2 space cos space 2 x y apostrophe open parentheses straight pi over 2 close parentheses equals 2 space cos space 2 open parentheses straight pi over 2 close parentheses y apostrophe open parentheses straight pi over 2 close parentheses equals 2 space cos space straight pi straight y apostrophe open parentheses straight pi over 2 close parentheses equals 2 open parentheses negative 1 close parentheses straight y apostrophe open parentheses straight pi over 2 close parentheses equals negative 2 less than 0  

Untuk interval fraction numerator 3 straight pi over denominator 4 end fraction less than x less than fraction numerator 5 straight pi over denominator 4 end fraction 

 x equals fraction numerator 5 straight pi over denominator 6 end fraction y apostrophe open parentheses fraction numerator 5 straight pi over denominator 6 end fraction close parentheses equals 2 space cos space 2 open parentheses fraction numerator 5 straight pi over denominator 6 end fraction close parentheses y apostrophe open parentheses fraction numerator 5 straight pi over denominator 6 end fraction close parentheses equals 2 space cos space open parentheses fraction numerator 5 straight pi over denominator 3 end fraction close parentheses y apostrophe open parentheses fraction numerator 5 straight pi over denominator 6 end fraction close parentheses equals 2 space cos space open parentheses 300 degree close parentheses y apostrophe open parentheses fraction numerator 5 straight pi over denominator 6 end fraction close parentheses equals 2 space cos space open parentheses 360 degree minus 60 degree close parentheses y apostrophe open parentheses fraction numerator 5 straight pi over denominator 6 end fraction close parentheses equals 2 space cos space open parentheses 60 degree close parentheses y apostrophe open parentheses fraction numerator 5 straight pi over denominator 6 end fraction close parentheses equals 2 space 1 half y apostrophe open parentheses fraction numerator 5 straight pi over denominator 6 end fraction close parentheses equals 1 greater than 0 

Jadi, grafik fungsi y equals sin space 2 x akan naik pada interval 0 less than x less than straight pi over 4 space atau space fraction numerator 3 straight pi over denominator 4 end fraction less than x less than 1 1 fourth straight pi. 

Oleh karena itu, jawaban yang benar adalah D. space       space 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Juli 2021

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