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

[cruisx]

Homework Statement

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

Homework Equations

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.

 

[VeeEight]

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?

 

[zachzach]

I got the same derivative.

 

[cruisx]

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?

 

[VeeEight]

Yup you solve both

 

[cruisx]

Yup you solve both

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)

 

[HallsofIvy]

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)

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