alleryFind the **maximum value** of $f(x) = \sin x + \cos x$ for $x \in [0, 2\pi]$.
A$1$
B$\sqrt 2$
C$2$
D$\pi$
Answer & Solution
Correct answer: B. $\sqrt 2$
$f(x) = \sin x + \cos x = \sqrt 2 \sin(x + \pi/4)$.
Max value = $\sqrt 2$, attained when $\sin(x + \pi/4) = 1$ ⇒ $x = \pi/4$.
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