Find all points of extrema on the interval [0, 2π] if y= x + sinx.

Dy/dx = 1 + cos(x). To find all extrema in [0, 2π], we set dy/dx = 0 to obtain: 0 = 1 + cos(x) ==> cos(x) = -1. This gives a solution of x = π on [0, 2π]. Therefore, the extrema on the intervals [0, 2π] is at x = π, which produces a point of (π, π). I hope this helps! θ βяια

 By taking derivatives: 

dy/dx = 1 + cos(x). 

To find all extrema in [0, 2π], we set dy/dx = 0 to obtain: 

0 = 1 + cos(x) 
==> cos(x) = -1. 

This gives a solution of x = π on [0, 2π]. 

Therefore, the extrema on the intervals [0, 2π] is at x = π, which produces a point of (π, π). 

I hope this helps!