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Application of Derivatives — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSApplication of Derivatives1 Mark
Question
Show that the function given by f (x) = sin x is decreasing in $\left(\frac{\pi}{2}, \pi\right)$
✓

Answer

The function is f (x) = sin x
Then, $f^\prime(x)=cosx$ 
Since for each x $\epsilon\left(\frac{\pi}{2}, \pi\right)$, cos x < 0, we have $f^\prime(x)<0$
Therefore, $f$ is strictly decreasing in$\left(\frac{\pi}{2}, \pi\right)$.

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