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Tentukan nilai maksimum dan nilai minimum dari fungsi f(x)=sinx−cosx !

Pertanyaan

Tentukan nilai maksimum dan nilai minimum dari fungsi f left parenthesis x right parenthesis equals sin x minus cos x !space space

R. Septa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai maksimum dan nilai minimum dari f left parenthesis x right parenthesis equals sin x minus cos x yakni square root of 2 space dan space minus square root of 2.

Pembahasan

Diketahui :

  • f left parenthesis x right parenthesis equals sin x minus cos x

Ditanya : nilai maksimum dan minimum fungsi f left parenthesis x right parenthesis equals sin x minus cos x

Jawab :

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell sin x minus cos x end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals 0 row cell cos x plus sin x end cell equals 0 row cell sin x end cell equals cell negative cos x end cell row cell fraction numerator sin x over denominator cos x end fraction end cell equals cell negative 1 end cell row cell tan x end cell equals cell negative 1 end cell row x equals cell 135 degree space atau space 315 degree end cell end table

 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis 135 degree right parenthesis end cell equals cell sin 135 degree minus cos 135 degree end cell row blank equals cell 1 half square root of 2 space minus open parentheses negative 1 half square root of 2 close parentheses end cell row blank equals cell 1 half square root of 2 space plus 1 half square root of 2 end cell row blank equals cell 2 over 2 square root of 2 space end cell row blank equals cell square root of 2 space left parenthesis nilai space maksimum right parenthesis end cell end table

 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis 135 degree right parenthesis end cell equals cell sin 315 degree minus cos 315 degree end cell row blank equals cell open parentheses negative 1 half square root of 2 close parentheses minus 1 half square root of 2 end cell row blank equals cell negative 2 over 2 square root of 2 space end cell row blank equals cell negative square root of 2 space left parenthesis nilai space minimum right parenthesis end cell end table

Dengan demikian, nilai maksimum dan nilai minimum dari f left parenthesis x right parenthesis equals sin x minus cos x yakni square root of 2 space dan space minus square root of 2.

100

4.7 (4 rating)

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