Question

Find all points of extrema on the interval [0, 2pi] if y=x+sinx
(-1.-1+(3pi/2))
(pi, pi)
(-1,0)
((3pi/2), 0)
none of these

I got pi as my critical number but I'm confused with the intervals.

Answer 1

dy/dx = 1 + cosx
= 0
cosx = -1
look at your cosine curve.
There is only one place where it has a value of -1 and it is at 180° or π radians for its entire period from 0 to 2π

so when x = π , back in the original equation:
y = π + sinπ
= π + 0 = π

so the point is (π,π)