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Tentukan interval fungsi begin mathsize 14px style y equals 1 third x cubed plus 2 x squared minus 5 x plus 1 end style naik.

A. Damanhuri

Master Teacher

Jawaban terverifikasi

Jawaban

fungsi begin mathsize 14px style y equals 1 third x cubed plus 2 x squared minus 5 x plus 1 end style naik pada interval begin mathsize 14px style x less than negative 5 space text atau end text space x greater than 1 end style.

Pembahasan

Diketahui fungsi begin mathsize 14px style y equals 1 third x cubed plus 2 x squared minus 5 x plus 1 end style.

Syarat fungsi naik adalah begin mathsize 14px style y apostrophe greater than 0 end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y apostrophe end cell greater than 0 row cell x squared plus 4 x minus 5 end cell greater than 0 row cell left parenthesis x plus 5 right parenthesis left parenthesis x minus 1 right parenthesis end cell equals 0 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell text atau end text end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 1 end table end style

Uji daerah dengan bantuan garis bilangan seperti berikut,

Jadi, fungsi begin mathsize 14px style y equals 1 third x cubed plus 2 x squared minus 5 x plus 1 end style naik pada interval begin mathsize 14px style x less than negative 5 space text atau end text space x greater than 1 end style.

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