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Math Help - stationary points

  1. #1
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    stationary points

    a) given y=e^-x cos x I found y'=-e^-x(sin x + cos x) and
    y"=2e^-x(sin x). I checked and they are right.

    b) find stationary points between -pi<x<pi and determine their nature.
    I can do this with simple quadratics but this function is beyond me at present.

    c) Find the points of inflection for -pi < x < pi

    Thank you for any help
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  2. #2
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    Quote Originally Posted by slaypullingcat View Post
    a) given y=e^-x cos x I found y'=-e^-x(sin x + cos x) and
    y"=2e^-x(sin x). I checked and they are right.

    b) find stationary points between -pi<x<pi and determine their nature.
    I can do this with simple quadratics but this function is beyond me at present.

    \textcolor{red}{-e^{-x}(\sin{x} + \cos{x}) = 0}

    \textcolor{red}{-e^{-x}} is always negative ... that means
    \textcolor{red}{\sin{x} = -\cos{x}} ... now, for what two values of x in the defined interval is that true?

    c) Find the points of inflection for -pi < x < pi

    \textcolor{red}{2e^{-x}\sin{x} = 0}

    same idea ... the only place where y'' = 0 in the given interval is at the endpoints and x = 0 .
    .
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  3. #3
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    sin 3pi/4=-cos 3pi/4 and sin pi/4=-cos pi/4 ? Is that correct?

    If so I just sub both values of x back into y to find the y coordinate?
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  4. #4
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    Quote Originally Posted by slaypullingcat View Post
    sin 3pi/4=-cos 3pi/4 (yes) and sin pi/4=-cos pi/4 (no)
    \sin\left(-\frac{\pi}{4}\right) = -\cos\left(-\frac{\pi}{4}\right)
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