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Tentukan nilai maksimum dan minimum dari fungsi-fu...

Tentukan nilai maksimum dan minimum dari fungsi-fungsi berikut.

b. begin mathsize 14px style f open parentheses x close parentheses equals x cubed plus 3 x squared minus 9 x plus 6 end style  

Jawaban:

begin mathsize 14px style f open parentheses x close parentheses equals x cubed plus 3 x squared minus 9 x plus 6 end style

begin mathsize 14px style f apostrophe open parentheses x close parentheses equals 3 x squared plus 6 x minus 9 f left parenthesis x right parenthesis space text stasioner end text space rightwards double arrow space f space apostrophe left parenthesis x right parenthesis equals 0 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x squared plus 6 x minus 9 end cell equals 0 row cell x squared plus 2 x minus 3 end cell equals 0 row cell open parentheses x plus 3 close parentheses open parentheses x minus 1 close parentheses end cell equals 0 end table end style

Diperoleh begin mathsize 14px style x equals negative 3 end style atau begin mathsize 14px style x equals 1 end style 

Nilai stasioner untuk begin mathsize 14px style x equals negative 3 end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses negative 3 close parentheses end cell equals cell 3 open parentheses negative 3 close parentheses cubed plus 3 open parentheses negative 3 close parentheses squared minus 9 open parentheses negative 3 close parentheses plus 6 end cell row blank equals cell 3 open parentheses negative 27 close parentheses plus 3 open parentheses 9 close parentheses plus 27 plus 6 end cell row blank equals cell negative 81 plus 27 plus 27 plus 6 end cell row blank equals cell negative 21 end cell end table end style

Nilai stasioner untuk begin mathsize 14px style x equals negative 1 end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 1 close parentheses end cell equals cell 3 open parentheses 1 close parentheses cubed plus 3 open parentheses 1 close parentheses squared minus 9 open parentheses 1 close parentheses plus 6 end cell row blank equals cell 3 plus 3 minus 9 plus 6 end cell row blank equals 3 end table end style 

Jadi, titik stasionernya adalah begin mathsize 14px style open parentheses negative 3 comma negative 21 close parentheses end style dan begin mathsize 14px style open parentheses negative 1 comma 3 close parentheses end style

Nilai maksimumnya adalah begin mathsize 14px style open parentheses negative 1 comma 3 close parentheses end style dan nilai minimumnya adalah begin mathsize 14px style open parentheses negative 3 comma negative 21 close parentheses end style.

 

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