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Choose the correct option.
The function f(x) = sin x + cos x, x ∈ (0, π/2); Maximum value of f(x) is:
The function $f(x) = \sin x + \cos x$, $x \in (0, \pi/2)$; Maximum value of $f(x)$ is:
- (a)1
- (b)2
- (c)$\frac{1}{\sqrt{2}}$
- (d)$\sqrt{2}$
Answer
Answer
Correct option: (d)
Answer: (d) $\sqrt{2}$
$f(x) = \sin x + \cos x = \sqrt{2}\sin\left(x + \frac{\pi}{4}\right)$, which is largest at $x = \frac{\pi}{4} \in \left(0, \frac{\pi}{2}\right)$.
Hence the maximum value is $\sqrt{2}$.