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Tentukan nilai maksimum dan minimum fungsi  pada interval .

Pertanyaan

Tentukan nilai maksimum dan minimum fungsi begin mathsize 14px style f open parentheses x close parentheses equals x to the power of 4 minus 4 x squared minus 6 end style pada interval begin mathsize 14px style negative 3 less or equal than x less or equal than 4 end style.

Pembahasan Video:

Pembahasan Soal:

Diketahui fungsi  begin mathsize 14px style f open parentheses x close parentheses equals x to the power of 4 minus 4 x squared minus 6 end style. Untuk menentukan nilai maksimum dan minimum, pertama-tama tentukan nilai stasioner begin mathsize 14px style f left parenthesis x right parenthesis end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals 0 row cell 4 x cubed minus 8 x end cell equals 0 row cell 4 x left parenthesis x squared minus 2 right parenthesis end cell equals 0 end table end style 

begin mathsize 14px style x equals 0 space text atau end text space x equals plus-or-minus square root of 2 end style

Terdapat 3 titik stasioner pada interval begin mathsize 14px style negative 3 less or equal than x less or equal than 4 end style.

Untuk begin mathsize 14px style x equals 0 end style maka

begin mathsize 14px style f left parenthesis 0 right parenthesis equals 0 to the power of 4 minus 4 left parenthesis 0 right parenthesis squared minus 6 equals negative 6 end style.

Untuk begin mathsize 14px style x equals plus-or-minus square root of 2 end style maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses square root of 2 close parentheses end cell equals cell open parentheses square root of 2 close parentheses to the power of 4 minus 4 open parentheses square root of 2 close parentheses squared minus 6 equals 4 minus 8 minus 6 equals negative 10 end cell row cell f open parentheses negative square root of 2 close parentheses end cell equals cell open parentheses negative square root of 2 close parentheses to the power of 4 minus 4 open parentheses negative square root of 2 close parentheses squared minus 6 equals 4 minus 8 minus 6 equals negative 10 end cell end table end style 

Tentukan juga nilai begin mathsize 14px style f left parenthesis negative 3 right parenthesis space text dan end text space f left parenthesis 4 right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 3 right parenthesis end cell equals cell left parenthesis negative 3 right parenthesis to the power of 4 minus 4 left parenthesis negative 3 right parenthesis squared minus 6 equals 81 minus 36 minus 6 equals 39 end cell row cell f left parenthesis 4 right parenthesis end cell equals cell 4 to the power of 4 minus 4 left parenthesis 4 right parenthesis squared minus 6 equals 256 minus 64 minus 6 equals 186 end cell end table end style 

Jadi, nilai maksimumnya adalah begin mathsize 14px style 186 end style dan nilai minimumnya adalah begin mathsize 14px style negative 10 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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