Question

I'm trying to find all the points on the graph y=4/3cos^3x-cosx where the tangent line is horizontal. I took the derivative, which gave me:

-4cos^2(x)sin(x)+sin(x)

Now I need to solve it for x and I'm not sure how. Can you help?

Answer 1

your derivative is ok

-4cos^2(x)sin(x)+sin(x) = 0
sinx( -4cos^2 x + 1 ) = 0
sinx = 0 ----> x = 0, ±π, ±2π, ...
or
4cos^2 x = 1
cos^2 x = 1/4
cosx = ± 1/2
so x is in any of the 4 quadrants
x = ±π/3, ±2π/3 , 4π/3, ±5π/3