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Homework Help: How to find local max and min points for y = sinxcox^3x

  1. Apr 22, 2010 #1
    1. The problem statement, all variables and given/known data

    Hey, so i need some help trying to find the local max and min points for y = sinxcox3x

    2. Relevant equations

    3. The attempt at a solution
    I know i need to find the first and 2nd derivative but i do not know if i am doing it right. I also do not know what to do after wards.

    my first derivative ends up being cos^2x(cos^2x - 3sin^2x)
    what do i do after this to solve my question. Help would be appreciated.
    Last edited: Apr 22, 2010
  2. jcsd
  3. Apr 22, 2010 #2
    You need to find the first derivative and check the values of x when Dy = 0 - so set your derivative to 0 and solve for x.
    I did not check your derivative. Did you apply the product rule?
  4. Apr 22, 2010 #3
    I got the same derivative.
  5. Apr 22, 2010 #4
    Yes my derivative is cos^2x(cos^2x - 3sin^2x) so do i do

    0 = cos^2x or 0 =cos^2x - 3sin^2x)

    and solve for both?
  6. Apr 22, 2010 #5
    Yup you solve both
  7. Apr 22, 2010 #6
    Ok so i got the values for the left but the right eqn is nto going well. I do not understand what to do after cos^2x - 3(1-cos^2x)
  8. Apr 23, 2010 #7


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    [itex]cos^2 x- 3 sin^2 x[/itex][itex]= cos^2 x- 3(1- cos^2 x)[/itex][itex]= cos^2 x- 3+ 3cos^2 x= 0[/itex]
    so [itex]4cos^2 x= 3[/itex], [itex]cos^2(x)= 3/4[/itex].
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