Maximum value? (1 Viewer)

rsingh

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Hey guys,

I always somehow take forever to do questions where they give you a fn and ask you to find it's max value.

e.g. 3cosx - 2sinx.

Do you just differentiate it, find the stationary pts and test is with the second deriivate, OR is there a quicker, alternative way?

Thanks guys.
 

shafqat

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You could collapse it into single trig function using auxiliary angle method.
 

Trev

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3cosx - 2sinx
rcos(x + α) [acosx - bsinx]
r = √(a²+b²) = √(9+4) = √13
tanα = b/a; α = whatever it is, don't have a calculator.
∴ = √13cos(x + α); differentiate that. EDIT: don't differentiate that :p
 
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acmilan

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the max value is just the amplitude, dont need to differentiate
 

rsingh

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Oh yeah it is!
Can't believe I forgot that?

Thanks acmilan!
 

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