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# Solution for Show That F(X) = Sin X Is Increasing on (0, π/2) and Decreasing on (π/2, π) and Neither Increasing Nor Decreasing in (0, π) ? - CBSE (Science) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

#### Question

Show that f(x) = sin x is increasing on (0, π/2) and decreasing on (π/2, π) and neither increasing nor decreasing in (0, π) ?

#### Solution

$\text { Here,}$

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

$\text { Domain of sin x is }\left( 0, \pi \right).$

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

$\text { For x } \in \left( 0, \frac{\pi}{2} \right), \cos x > 0 \left[ \because \cos x\text { is positive in first quadrant} \right]$

$f'\left( x \right) > 0$

$\text { So,f(x)is increasing for }\left( 0, \frac{\pi}{2} \right) .$

$\text { For x} \in \left( \frac{\pi}{2}, \pi \right), \cos x < 0 \left[ \because \cos x\text { is negative in second quadrant } \right]$

$\text { So,f(x)is decreasing for }\left( \frac{\pi}{2}, \pi \right).$

$\text { Since }f(x)\text { is increasing on } \left( 0, \frac{\pi}{2} \right) \text { and decreasing on}\left( \frac{\pi}{2}, \pi \right), f\left( x \right) \text { is neither decreasing nor increasing on }\left( 0, \pi \right).$

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#### Video TutorialsVIEW ALL [3]

Solution Show That F(X) = Sin X Is Increasing on (0, π/2) and Decreasing on (π/2, π) and Neither Increasing Nor Decreasing in (0, π) ? Concept: Increasing and Decreasing Functions.
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