Question

Identify the open intervals on which the function is increasing or decreasing.

Answer 1

ok

Answer 2

\[Cos^2(x) - \cos(x), 0 < x < 2\pi\]

Answer 3

are you taking calc 1?

Answer 4

Apologies, I didn't realize this posted before I could add in the equation. I graphed this in Geogebra and from there, it looks like there's 14 different answers... I'm not sure if I'm supposed to give them every interval or not

And yes, I'm taking calc 1

Answer 5

yeah , can you find the derivative of that function

Answer 6

Yeah, I've got sin(x) -2xsin(x^2)

Answer 7

y' = -2sin(x)cos(x) + sin(x)

Answer 8

set that to zero and find out which points are needed for testing if the function is increasing/decreasing

Answer 9

i can see pi and 2pi will be a couple of the solutions, there are 2 more

Answer 10

sin(pi) and sin(2pi) = 0

Answer 11

(5/3)pi is also a solution , critical point

Answer 12

and 1/3 pi

Answer 13

is 1/5 pi a solution as well?

Answer 14

no

Answer 15

so..

Answer 16

you have to test if the function is increasing or decreasing in each of those intervals,
(0, 1/3 pi)
(1/3 pi, pi)
(pi, 5/3pi)
(5/3pi, 2pi)

Answer 17

Hmm okay it's a bit clearer now. I messed myself up at the beginning because I read cos^2(x) as cos(x^2) and then everything was downhill from there.

Answer 18

did you graph it?

Answer 19

(0, 1/3 pi) - decr
(1/3 pi, pi) - incr
(pi, 5/3pi) - decr
(5/3pi, 2pi) -incr