Question

Find all points on the graph of the function f(x) = 2 cos(x) + (cos(x))2 at which the tangent line is horizontal. Consider the domain x = [0,2π).

[ ,] (Smaller x values)
[ , ] (Larger x values)

Answer 1

did you try to find first derivative (if you can use calculus...) & =0 ?

Answer 2

I just don't understand this problem. I tried setting it up but it doesn't work.

Answer 3

f(x) = 2cos(x) + cos^2(x)
f'(x) = -2sin(x) - 2cos(x)sin(x)

-2sin(x) - 2cos(x)sin(x) = 0
sin(x) + cos(x)sin(x) = 0
sin(x)(1 + cos(x)) = 0
sin(x) = 0, 1 + cos(x) = 0

Answer 4

that's what i have done so far

Answer 5

looks good to me!
I got the same & it gave me:
x=0 & x=pi

Answer 6

so i got (0,3) and (pi, -1)

Answer 7

me too :)
i hope it's the right answer