Find coordinate points where the tangent line is horizontal for

kejpsy 2022-01-26 Answered
Find coordinate points where the tangent line is horizontal for f(x)=sin(8x)+6cos(4x)8x
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Expert Answer

Palandriy0
Answered 2022-01-27 Author has 14 answers

You have used the wrong double angle formula, it should be
cos8x=12sin2(4x)
and corresponding quadratic equation would be 2u23u2=0 and at last you would get sin4x=12

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pacetfv
Answered 2022-01-28 Author has 9 answers
Let
g(x)=f(x4)=sin2x+6cosx2x
Then
g(x)=2cos2x6sinx2
=2(12sin2x)6sinx2
=2(2sin2x3sinx2)
=2(2sinx+1)(sinx2)
Hence the critical points of g occur when sinx=12 (it is not possible for sinx=2). There are four such x(π,2π)
x{5π6,π6,7π6,11π6}
Consequently, the critical points of f occur when sin4x=12, and for π4<x<π2, this occurs at
x{5π24,π24,7π24,11π24}
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