Question

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

Answer 1

Increasing when y'>0, decreasing when y'<0

Answer 2

\[f(x)=\cos^2(x)\]
\[f ' (x)=-2\sin(x)\cos(x)\]

Answer 3

Is that using the derivative?
I have to show sign analysis

Answer 4

Set the derivative equal to 0 and solve.

Answer 5

Then you'll get some values suppose when y'=0, x1=a, x2=b, x3=c.
Create something like a table like the one I'll show you, very helpful...

Answer 6

Am I suppose to do
-2sin(x)cos(x)>0 to find where it is increasing?

Answer 7

By the way, those are just made up functions.