Pertanyaan

Tentukan interval turun fungsi f ( x ) = x − 1 x 2 − 7 x + 10 .

Tentukan interval turun fungsi $f (x) = \frac{x ^{2} - 7 x + 10}{x - 1}$ .

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Perhatikan Ingat sehingga Berdasarkan grafik di atas, interval turun fungsi saat .

Perhatikan

$f open parentheses x close parentheses equals fraction numerator x squared minus 7 x plus 10 over denominator x minus 1 end fraction$

Ingat

$f open parentheses x close parentheses equals u over v f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction$

sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x squared minus 7 x plus 10 end cell row v equals cell x minus 1 end cell row cell u apostrophe end cell equals cell 2 x minus 7 end cell row cell v apostrophe end cell equals 1 row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator open parentheses 2 x minus 7 close parentheses open parentheses x minus 1 close parentheses minus 1 open parentheses x squared minus 7 x plus 10 close parentheses over denominator open parentheses x minus 1 close parentheses squared end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 2 x squared minus 9 x plus 7 minus x squared plus 7 x minus 10 over denominator open parentheses x minus 1 close parentheses squared end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator x squared minus 2 x minus 3 over denominator open parentheses x minus 1 close parentheses squared end fraction end cell row 0 equals cell fraction numerator x squared minus 2 x minus 3 over denominator open parentheses x minus 1 close parentheses squared end fraction end cell row x equals cell negative 1 comma space x equals 3 comma space x not equal to 1 end cell end table$

Berdasarkan grafik di atas, interval turun fungsi $f open parentheses x close parentheses equals fraction numerator x squared minus 7 x plus 10 over denominator x minus 1 end fraction$ saat negative 1 less or equal than x less than 1 space union space 1 less than x less or equal than 3 .