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# Solution for Find the Intervals in Which F(X) is Increasing Or Decreasing F(X) = Sinx + |Sinx|, 0 < X ≤ 2 π ? - CBSE (Commerce) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Find the interval in which f(x) is increasing or decreasing f(x) = sinx + |sin x|, 0 < x $\leq 2\pi$ ?

#### Solution

$f\left( x \right) = \sin x + \left| \sin x \right|, 0 < x \leq 2\pi$

$\text { Case I: When x }\in \left( 0, \pi \right)$

$f\left( x \right) = \sin x + \sin x = 2\sin x$

$\Rightarrow f'\left( x \right) = 2\cos x$

$\text { As,} \cos x > 0 \text { for } x \in \left( 0, \frac{\pi}{2} \right) \text { and }\cos x < 0 \text { for } x \in \left( \frac{\pi}{2}, \pi \right)$

$\text { So,} f'\left( x \right) > 0\text { for} x \in \left( 0, \frac{\pi}{2} \right)\text{ and } f'\left( x \right) < 0 \text { for }x \in \left( \frac{\pi}{2}, \pi \right)$

$\therefore f\left( x \right)\text { is increaing on} \left( 0, \frac{\pi}{2} \right) \text { and } f\left( x \right) \text { is decreasing on } \left( \frac{\pi}{2}, \pi \right) .$

$\text { Case II: When x } \in \left( \pi, 2\pi \right)$

$f\left( x \right) = \sin x - \sin x = 0$

$\Rightarrow f'\left( x \right) = 0$

$\text { So,} f\left( x \right) \text { is neither increaing nor decreasing on } \left( \pi, 2\pi \right) .$

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Solution Find the Intervals in Which F(X) is Increasing Or Decreasing F(X) = Sinx + |Sinx|, 0 < X ≤ 2 π ? Concept: Increasing and Decreasing Functions.
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