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Jika nilai minimum fungsi adalah , maka nilai maks...

Jika nilai minimum fungsi f left parenthesis x right parenthesis equals a squared cos left parenthesis x right parenthesis plus a adalah 1 fourth, maka nilai maksimum f(x) adalah.....

  1. 1 half

  2. 3 over 4

  3. 1

  4. 5 over 4

  5. 4

Jawaban:

straight f open parentheses straight x close parentheses equals straight a squared cos space straight x plus straight a rightwards arrow box enclose negative straight a squared plus straight a less or equal than straight f open parentheses straight x close parentheses less or equal than straight a squared plus straight a end enclose  Maka space nilai space minimum space straight f left parenthesis straight x right parenthesis space adalah space box enclose negative straight a squared plus straight a end enclose.  Sehingga  space space space space space space minus straight a squared plus straight a equals 1 fourth  space space minus 4 straight a squared plus 4 straight a equals 1  4 straight a squared minus 4 straight a plus 1 equals 0  space space space space space space open parentheses 2 straight a minus 1 close parentheses squared equals 0  space space space space space space space space space space 2 straight a minus 1 equals 0  space space space space space space space space space space space space space space space space 2 straight a equals 1  space space space space space space space space space space space space space space space space space space box enclose straight a equals 1 half end enclose    Nilai space maksimum space untuk space straight f left parenthesis straight x right parenthesis space adalah space straight a squared plus straight a.  Karena space straight a equals 1 half comma space maka  maks straight space straight f open parentheses straight x close parentheses equals straight a squared plus straight a equals open parentheses 1 half close parentheses squared plus 1 half equals 1 fourth plus 1 half equals box enclose 3 over 4 end enclose

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