Fungsi f(x)=sin2x+(2x),x>0 turun pada interval ....

Pertanyaan

Fungsi $\style{font-size:14px}{f(x)=\sqrt{\sin^2x+\left(\frac x2\right)},\;x>0}$ turun pada interval ....

$begin mathsize 14px style fraction numerator 5 straight pi over denominator 12 end fraction less than x less or equal than fraction numerator 13 straight pi over denominator 12 end fraction end style$
$begin mathsize 14px style fraction numerator 7 straight pi over denominator 12 end fraction less than x less than fraction numerator 11 straight pi over denominator 12 end fraction end style$
$begin mathsize 14px style straight pi over 12 less than x less or equal than fraction numerator 5 straight pi over denominator 12 end fraction end style$
$begin mathsize 14px style fraction numerator 7 straight pi over denominator 6 end fraction less than x less or equal than fraction numerator 13 straight pi over denominator 6 end fraction end style$
$begin mathsize 14px style fraction numerator 7 straight pi over denominator 6 end fraction less than x less or equal than fraction numerator 11 straight pi over denominator 6 end fraction end style$

Pembahasan:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell square root of sin squared x plus left parenthesis x over 2 right parenthesis end root comma space x greater than 0 end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator sin space 2 x space plus begin display style 1 half end style over denominator 2 square root of sin squared x plus left parenthesis x over 2 right parenthesis end root end fraction less than 0 end cell end table end style$

Sehingga diperoleh $begin mathsize 14px style f left parenthesis x right parenthesis end style$ turun pada interval:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 2 x space plus 1 half end cell less than cell 0 space end cell row cell sin space 2 x end cell less than cell negative 1 half space end cell row cell fraction numerator 7 straight pi over denominator 6 end fraction end cell less than cell 2 x less than fraction numerator 11 straight pi over denominator 6 end fraction end cell row cell space fraction numerator 7 straight pi over denominator 12 end fraction end cell less than cell x less than fraction numerator 11 straight pi over denominator 12 end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah B.

Jawaban terverifikasi

Dijawab oleh:

Terakhir diupdate 06 Oktober 2021