If f(x)=2(7cosx+24sinx)(7sinx-24cosx), then find the maximum value of (f(x))^1/4

Asked by aahnik.mohanty | 22nd May, 2019, 09:59: PM

Expert Answer:

f(x)=2(7cosx+24sinx)(7sinx-24cosx)
Multiply and divide f(x) by 25, we get
 
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Let space 7 over 25 space equals space cosα space and space fraction numerator 24 over denominator space 25 end fraction space equals space sinα
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rightwards double arrow space space straight f left parenthesis straight x right parenthesis space equals 25 space cross times space 25 space cross times sin open square brackets 2 open parentheses straight x space minus space straight alpha space close parentheses close square brackets
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We space know space that space sin space function space has space the space maximum space value space as space 1.
Therefore space the space maximum space value space of space straight f left parenthesis straight x right parenthesis space is space
rightwards double arrow space space straight f left parenthesis straight x right parenthesis space equals 25 space cross times space 25 space cross times 1 space equals space 625
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Answered by Yasmeen Khan | 23rd May, 2019, 11:08: AM

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