For the function $f(x) = \sin x + \cos x, x ∈ [0,π]$, which one of the following is correct?

Absolute maximum value is $\sqrt{2}$

The correct answer is Option (2) → Absolute maximum value is $\sqrt{2}$

$f(x)=\sin x+\cos x,\;x\in[0,\pi]$

$\frac{df}{dx}=\cos x-\sin x$

Critical point from $\cos x-\sin x=0$

$\tan x=1$

$x=\frac{\pi}{4}$

Evaluate $f(x)$ at $x=0,\;\frac{\pi}{4},\;\pi$

$f(0)=1$

$f\left(\frac{\pi}{4}\right)=\sqrt2$

$f(\pi)=-1$

Hence absolute maximum value is $\sqrt2$

The correct statement is: Absolute maximum value is $\sqrt2$.