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A function  i.   Function drops at interval  ii.  Function increases at intervals  iii. Minimum turning point  iv. Maximum value  The true statements are....

Pertanyaan

A function f open parentheses x close parentheses equals x cubed plus 6 x squared minus 15 x plus 3

i.   Function drops at interval negative 5 less than x less than 1

ii.  Function increases at intervals x less than 1

iii. Minimum turning point open parentheses 1 comma negative 5 close parentheses

iv. Maximum value equals space 5

The true statements are....

  1. i and iispace

  2. i and iiispace

  3. i and ivspace

  4. ii and ivspace

  5. iii and ivspace

Pembahasan Soal:

Diketahui

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell x cubed plus 6 x squared minus 15 x plus 3 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 3 x squared plus 12 x minus 15 end cell end table

( i ) Fungsi turun ketika f apostrophe open parentheses x close parentheses less than 0

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell less than 0 row cell 3 x squared plus 12 x minus 15 end cell less than 0 row cell x squared plus 4 x minus 5 end cell less than 0 row cell open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end cell less than 0 row cell negative 5 end cell less than cell x less than 1 end cell end table

Dengan demikian fungsi f open parentheses x close parentheses turun pada interval negative 5 less than x less than 1.

( ii ) Fungsi turun ketika f apostrophe open parentheses x close parentheses greater than 0

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell greater than 0 row cell 3 x squared plus 12 x minus 15 end cell greater than 0 row cell x squared plus 4 x minus 5 end cell greater than 0 row cell open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end cell greater than 0 row x less than cell negative 5 space atau space x greater than 1 end cell end table

Dengan demikian fungsi f apostrophe open parentheses x close parentheses naik pada interval x less than negative 5 space atau space x greater than 1.

( iii ) Nilai minimum fungsi

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals 0 row cell 3 x squared plus 12 x minus 15 end cell equals 0 row cell x squared plus 4 x minus 5 end cell equals 0 row cell open parentheses x plus 5 close parentheses open parentheses x minus 1 close parentheses end cell equals 0 row cell x plus 5 end cell equals cell 0 space atau space x minus 1 equals 0 end cell row x equals cell negative 5 space atau space x equals 1 end cell end table

Ketika x equals negative 5

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses negative 5 close parentheses end cell equals cell open parentheses negative 5 close parentheses cubed plus 6 open parentheses negative 5 close parentheses squared minus 15 open parentheses negative 5 close parentheses plus 3 end cell row blank equals cell negative 125 plus 150 plus 75 plus 3 end cell row blank equals 103 end table

Ketika x equals 1

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 1 close parentheses end cell equals cell open parentheses 1 close parentheses cubed plus 6 open parentheses 1 close parentheses squared minus 15 open parentheses 1 close parentheses plus 3 end cell row blank equals cell 1 plus 6 minus 15 plus 3 end cell row blank equals cell negative 5 end cell end table

Maka titik balik minimum adalah open parentheses 1 comma negative 5 close parentheses.

( iv ) Dari perhitungan pada poin ( iii ) diperoleh nilai maksimum adalah 103.

Dengan demikian pernyataan yang benar adalah ( i ) dan ( iii ).

Oleh karena itu, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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