posted by sh on .
Find the interval(s) where the function is increasing where and it is decreasing.
f(x)=sin(x+(pi/2)) for 0≤x≤2pi
so my derivative is f'(x)=cos(x+(pi/2))?
and my critical number is -pi/2?
cosine is positive for x +pi/2 = 0 to pi/2 and from 3 pi/2 to 2 pi
when x+pi/2 = 0 then x = -pi/2 or 3pi/2
when x + pi/2 = pi/2, x = 0
so one interval is x = 3pi/2 to 0
when x+pi/2 = 3 pi/2 then x = pi
when x+pi/2 = 2 pi then x = 3 pi/2
so second interval is frm x = pi to 3 pi/2
so finally the entire interval from x = pi to x = 2 pi (which is 0) has a positive derivative, function increasing
Wow, so confusing. Thanks!
So the whole interval is increasing? The function of cosx has a section of decreasing though.