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Jika f ( x ) = sin x cos 2 x ​ maka nilai dari f ( 4 π ​ )

Jika  maka nilai dari  

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R. Novianto

Master Teacher

Mahasiswa/Alumni Universitas Tanjungpura Pontianak

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Diketahui : Ditanya :nilai dari ? Dijawab :

Diketahui : begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator cos squared space straight x over denominator sin space straight x end fraction end style 

Ditanya : nilai dari begin mathsize 14px style straight f apostrophe open parentheses straight pi over 4 close parentheses end style  ?

Dijawab :

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell straight f open parentheses straight x close parentheses end cell equals cell fraction numerator cos squared straight x over denominator sin space straight x end fraction end cell row straight u equals cell cos squared straight x end cell row cell straight u apostrophe end cell equals cell 2 space cos space straight x times negative sin space straight x end cell row straight v equals cell sin space straight x end cell row cell straight v apostrophe end cell equals cell cos space straight x end cell row blank blank blank row cell straight f apostrophe open parentheses straight x close parentheses end cell equals cell straight u over straight v end cell row cell straight f apostrophe open parentheses straight x close parentheses end cell equals cell fraction numerator straight u apostrophe straight v minus uv apostrophe over denominator straight v squared end fraction end cell row blank equals cell fraction numerator negative 2 space cos space straight x times sin space straight x open parentheses sin space straight x close parentheses minus cos squared straight x open parentheses cos space straight x close parentheses over denominator sin squared space straight x end fraction end cell row cell straight f apostrophe open parentheses straight pi over 4 close parentheses end cell equals cell fraction numerator negative 2 space cos space open parentheses straight pi over 4 close parentheses times sin space open parentheses straight pi over 4 close parentheses open parentheses sin space open parentheses straight pi over 4 close parentheses close parentheses minus cos squared open parentheses straight pi over 4 close parentheses open parentheses cos space open parentheses straight pi over 4 close parentheses close parentheses over denominator sin squared space open parentheses straight pi over 4 close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses negative up diagonal strike 2 times begin display style fraction numerator 1 over denominator up diagonal strike 2 end fraction end style square root of 2 times 1 half square root of 2 times 1 half square root of 2 close parentheses minus open parentheses 1 half square root of 2 times 1 half square root of 2 times 1 half square root of 2 close parentheses over denominator 1 half square root of 2 times 1 half square root of 2 end fraction end cell row blank equals cell fraction numerator begin display style 2 over 4 end style square root of 2 minus begin display style 4 over 8 end style square root of 2 over denominator begin display style 2 over 4 end style end fraction end cell row blank equals cell fraction numerator 0 over denominator 2 over 4 end fraction end cell row blank equals 0 end table end style 

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Salah satu titik stasioner dari fungsi f ( x ) = 2 ​ − cos x sin x ​ dengan 0 < x ≤ π adalah ....

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