Application of Derivatives — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
Question
Show that the function given by f (x) = sin x is neither increasing nor decreasing in (0, $\pi$)
✓
Answer
The function is f (x) = sin x Then, $f^\prime$(x) = cos x Since for each x $\in$ $\left(0, \frac{\pi}{2}\right)$, cos x > 0, we have $f^\prime(x)$ >0 Therefore, $f$ is strictly increasing in$\left(0, \frac{\pi}{2}\right)$……(1) Now, The function is f (x) = sin x Then, $f^\prime(x)=cosx$ Since, for each $x\in\left(\frac{\pi}{2}, \pi\right)$, cos x < 0, we have $f^\prime(x)$ < 0 Therefore, $f$ is strictly decreasing in $\left(\frac{\pi}{2}, \pi\right)$……(2) From (1) and (2), It is clear that f is neither increasing nor decreasing in (0, $\pi$).
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