Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:

f (x) = sin x + cos x, x ∈ [0, π]

It is given that f (x) = sin x + cos x, x ∈ [0, π]

f’(x) = cosx - sinx

Now, f’(x) = 0

⇒ cosx - sinx = 0

⇒ cosx = sinx

⇒ tanx = 1

⇒ x =

Now, we evaluate the value of f at critical point and at end points of the interval [0, π]

f(0) = sin0 +cos0 = 0+1 = 1

f(π) = sin π + cos π = 0 -1 = -1

Therefore, we have the absolute maximum value of f on [0, π] is √2 occurring at

And, the absolute minimum value of f on [0, π] is -1 occurring at x = π.