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Homework Help: Sketching A Graph Using Differentiation

  1. Sep 5, 2010 #1
    1. The problem statement, all variables and given/known data

    attachment.php?attachmentid=28017&stc=1&d=1283735934.jpg

    2. Relevant equations



    3. The attempt at a solution

    I don't understand how they get from step 4 to step 5. Wouldn't you factor a cos x out of the brackets then have [tex](\cos x)(1-\frac{1}{6})[/tex] to the left of the brackets. Then you can multiply the [tex](1-\frac{1}{6})[/tex] inside the brackets.However that would yield [tex][\frac{5}{6}+\frac{10}{3}\sin^2x][/tex] I dont understand how they are getting 1- (1/6) times the stuff inside the brackets.
     

    Attached Files:

    Last edited: Sep 5, 2010
  2. jcsd
  3. Sep 6, 2010 #2
    [tex]\cos x - \frac{1}{6}[(1-2\sin^2 x)\cos x - 2\sin^2 x\cos x][/tex]

    [tex]= \cos x - \frac{1}{6}[ \cos x (1-2\sin^2 x - 2\sin^2 x) ][/tex]

    [tex]= \cos x - \frac{1}{6} \cos x(1-2\sin^2 x - 2\sin^2 x)[/tex]

    [tex]= \cos x [ 1 - \frac{1}{6}(1-2\sin^2 x - 2\sin^2 x) ][/tex]
     
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