I need help with this problem
find all extrema in the interval [0, 2pi] for y=x - cos x. (write as points and mark each point as absolute, relative, or both)
the first thing i did was to find the derivative of y=x - cos x. i did this and got dy/dt=1 +sin x. I then set this equal to 0 to find the critical points (i know that i didn't need to check where the derivative is undefined because it is defined at all x values since there is no denominator). The critical point i got was 3pi/2.
I then plugged in my two endpoints (0 & 2pi) and my critical point (3pi/2) into the original equation to get the y values at each point. I got (0, -1), (2pi, 5.2831), and (3pi,2,4.7123).
I'm pretty sure my points are right, but I don't know what they mean. I'm pretty sure that 0 is a relative min but can i also call it an absolute min? Are 3pi/2 and 2pi relative maxes? and can i call 2pi an absolute max?