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Diketahui fungsi h(x)=−x3−15x2−27x+1. Fungsi h(x) naik pada interval ...

Pertanyaan

Diketahui fungsi begin mathsize 14px style h left parenthesis x right parenthesis equals negative x cubed minus 15 x squared minus 27 x plus 1 end style. Fungsi size 14px h size 14px left parenthesis size 14px x size 14px right parenthesis naik pada interval ...

  1. size 14px x size 14px less than size 14px minus size 14px 9 size 14px space size 14px atau size 14px space size 14px x size 14px greater than size 14px minus size 14px 1 

  2. size 14px x size 14px less than size 14px minus size 14px 9 size 14px space size 14px atau size 14px space size 14px x size 14px greater than size 14px 1 

  3. size 14px x size 14px less than size 14px 1 size 14px space size 14px atau size 14px space size 14px x size 14px greater than size 14px 9 

  4. size 14px minus size 14px 9 size 14px space size 14px less than size 14px x size 14px less than size 14px 1   

  5. undefined 

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E

Pembahasan

Ingat bahwa fungsi naik, jika begin mathsize 14px style h apostrophe left parenthesis x right parenthesis greater than 0 end style.

Diketahui fungsi begin mathsize 14px style h left parenthesis x right parenthesis equals negative x cubed minus 15 x squared minus 27 x plus 1 end style. Akan ditentukan interval jika fungsi size 14px h size 14px left parenthesis size 14px x size 14px right parenthesis naik.

Terlebih dahulu tentukan turunan dari fungsi tersebut.

table attributes columnalign right center left columnspacing 2px end attributes row cell h open parentheses x close parentheses end cell equals cell negative x cubed minus 15 x squared minus 27 x plus 1 end cell row cell h apostrophe open parentheses x close parentheses end cell equals cell negative 3 x to the power of 3 minus 1 end exponent minus 15 times 2 times x to the power of 2 minus 1 end exponent minus 27 end cell row cell h apostrophe open parentheses x close parentheses end cell equals cell negative 3 x squared minus 30 x minus 27 end cell end table

Karena fungsi naik, Maka begin mathsize 14px style h apostrophe left parenthesis x right parenthesis greater than 0 end style, sehingga diperoleh:

table attributes columnalign right center left columnspacing 2px end attributes row cell negative 3 x squared minus 30 x minus 27 end cell greater than 0 row cell kedua space ruas space dikali space open parentheses negative 1 close parentheses end cell blank blank row cell 3 x squared plus 30 x plus 27 end cell less than 0 row cell kedua space ruas space dibagi space 3 end cell blank blank row cell x squared plus 10 x plus 27 end cell less than 0 row cell open parentheses x plus 9 close parentheses open parentheses x plus 1 close parentheses end cell less than 0 row cell x plus 9 space greater than 0 end cell blank cell x plus 1 less than 0 end cell row cell x greater than negative 9 end cell blank cell x less than negative 1 end cell row cell negative 9 less than x less than negative 1 end cell blank blank end table

Sehingga diperoleh fungsi size 14px h size 14px left parenthesis size 14px x size 14px right parenthesis naik pada interval begin mathsize 14px style negative 9 less than x less than negative 1 end style.

Oleh karena itu, jawaban yang tepat adalah E

680

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