Grafik fungsi f(x)=31x3+27x2−18x+4 turun pada interval ...

Pertanyaan

Grafik fungsi $\style{font-size:14px}{f\left(x\right)=\frac13x^3+\frac72x^2-18x+4}$ turun pada interval ...

$begin mathsize 14px style negative 9 less than x less than 2 end style$
$begin mathsize 14px style negative 2 less than x less than 9 end style$
$begin mathsize 14px style x less than negative 9 space atau space x greater than 2 end style$
$begin mathsize 14px style x less than negative 2 space atau space x greater than 9 end style$
$size 14px x size 14px less than size 14px 2 size 14px space size 14px atau size 14px space size 14px x size 14px greater than size 14px 9$

Pembahasan:

Perhatikan perhitungan berikut.

Ingat, fungsi turun:

$begin mathsize 14px style f apostrophe open parentheses x close parentheses less than 0 end style$

Maka:

$begin mathsize 14px style f left parenthesis x right parenthesis equals 1 third x cubed plus 7 over 2 x squared minus 18 x plus 4 f apostrophe open parentheses x close parentheses equals 3 over 3 x to the power of 3 minus 1 end exponent plus fraction numerator 7 times 2 over denominator 2 end fraction x to the power of 2 minus 1 end exponent minus 18 f apostrophe left parenthesis x right parenthesis equals x squared plus 7 x squared minus 18 end style$

sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus 7 x squared minus 18 end cell less than 0 row cell open parentheses x plus 9 close parentheses open parentheses x minus 2 close parentheses end cell less than 0 end table end style$

Didapatkan $begin mathsize 14px style x equals negative 9 end style$ atau $undefined$ . Bentuk garis bilangan.

Ujikan titik $begin mathsize 14px style x equals 0 end style$ , maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x plus 9 close parentheses open parentheses x minus 2 close parentheses end cell less than 0 row cell open parentheses 0 plus 9 close parentheses open parentheses 0 minus 2 close parentheses end cell less than 0 row cell 9 open parentheses negative 2 close parentheses end cell less than 0 row cell negative 18 end cell less than 0 end table end style$

Sehingga