find the minimum and maximum value of sin x + cos x

How do you find the maximum and minimum value of $f$$($$x$$)$$=$$\sin$$x$$+$$\cos$$x$

Consider the general term :-

 $f\left(x\right)=\mathrm{a.sin}x+\mathrm{b.cos}x$.

From this :;

We can find the maximum and minimum value of $f\left(x\right)=\sin x+\mathrm{cos\; x}$

Which is +2½ and -2½ respectively. Taking a=1 and b=1 .