maximum and minimum of y = cos(x) + sin (x)on the interval [0,2pi]

Answer 1

Let
f(x) = cos(x) + sin (x)
Calculate derivative f'(x) and equate to zero. Solve for x.
For each value x1 of the solution, verify
f''(x). f''(x)<0 = maximum, and f''(x)>0 = minimum.
There may be multiple maxima and minima, choose the extreme values.

Answer 2

would the max be sqrt(2) at x = pi/4, and the min be -sqrt(2) at x = 5pi/4?

Answer 3

Exactly! where tan(x)=1.

Answer 4

thank you very much

Answer 5

You're welcome!