Application of Derivatives — MATHS STD 12 Science — Question
Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSApplication of Derivatives1 Mark
Question
Prove that the function given by f(x) = cos x is neither increasing nor decreasing in (0, 2$\pi$).
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Answer
Note that $f ′(x) = – sin x$ Clearly, for $$$(0, \pi)$, we have $f ′(x) = – sin x<0$ So, the function is decreasing in $(0, \pi)$. Now, for $x \in (\pi, 2\pi)$ we have $f ′(x) = – sin x>0$ Therefore, $f(x)$ is increasing in $(\pi, 2\pi)$ Hence, f is neither increasing nor decreasing in (0, 2$\pi$).
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