The absolute maximum value of the function $f(x)=sinx+cosx, x \in [0, \pi]$ is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\sqrt{2}$
$f(x)=\left(\frac{1}{\sqrt{2}}\sin x+\frac{1}{\sqrt{2}}\cos x\right)^{\sqrt{2}}$
$=\sqrt{2}(\sin x\cos(π/4)+\cos x\sin(π/4))$
$=\sqrt{2}\sin(x+π/4)$ $x∈[0,π]$
at $x=π/4$ max. exists
$f(π/4)=f_{max}=\sqrt{2}$