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Thread: First derivative test, local min/max

  1. #1
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    First derivative test, local min/max

    Hi

    I have a function

    $\displaystyle g(x)=(cos \ x + sin \ x - 1)e^{cos x + sin x} \ \ \ \ \ (0 \leq x \leq\pi)$

    the derivative being

    $\displaystyle g`(x)=(cos^2 \ x - sin^2 \ x)e^{cos x + sin x}$

    I'm not sure how to find the turning point within this domain.

    Any ideas?
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  2. #2
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    Krizalid's Avatar
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    $\displaystyle g'(x)=\left( \cos ^{2}x-\sin ^{2}x \right)e^{\cos x+\sin x}=0,$ and this is just $\displaystyle \cos ^{2}x-\sin ^{2}x=0$ since $\displaystyle e^{\cos x+\sin x}>0$ for each $\displaystyle x\in\mathbb R.$ Now find solutions for $\displaystyle 0\le x\le\pi$ for that trig. equation.
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  3. #3
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    This could simply things.
    $\displaystyle \cos ^2 (x) - \sin ^2 (x) = \cos (2x)$
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