Question

Find the intervals on which f is increasing and decreasing. f(x)=-5cos^2x on [-pi,pi].

Answer 1

Screenshot of problems with correct answer.

Answer 2

find f'(x).
if f'(x)>0 in (a,b), then f(x) is increasing for x belongs to (a,b).
if f'(x)<0, f decreases in that interval.

Answer 3

Yeah i understand what i'm supposed to do, however the trig is messing me up. I got to 0=10cosxsinx. Not sure where to go from there.

Answer 4

f'(x)=10sinxcosx=5sin2x.
f'(x)=sin2x.
now find the intervals where 2sin2x>0

Answer 5

I don't see how you simplified it to 5sin(2x) and then just sin2x?

Answer 6

Oh wait is that the double angle identity?

Answer 7

yes it is.

Answer 8

Okay so now we have sin2sx=0 How do i find the intervals? Also why did you add a 2 in from of sin2x?

Answer 9

oh sorry, it was 5sin2x>0.
just a typing mistake. my bad.

Answer 10

Then you divide the 5 out so you'll left with sin2x. Not sure how to go on from here.