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Math Help - Critical numbers

  1. #1
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    Critical numbers

    This is just a practice quiz, but I want to know how to do it for when I take the test. Here is my question:

    http://i42.tinypic.com/im3q53.jpg

    Thanks!

    EDIT: I meant I graphed it as 2(1/cosx) +tanx
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  2. #2
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    \frac{d}{dx}(2\sec \theta + \tan \theta)=\frac{1}{\cos ^2 x}(2\sin x +1)=0 \Longleftrightarrow \sin x = -\frac{1}{2}
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  3. #3
    MHF Contributor Calculus26's Avatar
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    convert to sines and cosines

    2sin(t) = -1

    t= 7pi/6 and 11pi/6

    Seems who ever made the answer key was trying to be cute --A and B are coterminal with 7pi/6 and 11pi/6

    Technical point -- a stationary point is where the derivative is 0

    A critical point is where the derivative is either 0 or undefined

    The point is a critical point represents where the sign of the derivative can change signs either where it is 0 or undefined

    For example |x| has a critical point at 0 even though it has no derivative there

    Also the derivative is undefined at pi/2 which would make it a critcal number also this would make c a viable answer as well
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Correction

    Since f is not defined at pi/2 --it is not a critical point

    |x| is defined at 0 but its derivative is not
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