CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsDifferentiation and it's Applications1 Mark
MCQ
Which of the following functions is decreasing on $\left(0, \frac{\pi}{2}\right)$.
A
sin 2x
B
tan x
✓
cos x
D
cos 3x
✓
Answer
Correct option: C.
cos x
(C) cos x Explanation: In the given interval $\left(0, \frac{\pi}{2}\right)$ f(x) = cos x On differentiating w.r.t. x, we get f'(x) = - sin x which gives $f^{\prime}(x)<0$ in $\left(0, \frac{\pi}{2}\right)$ Hence, f(x) = cos x is decreasing in $\left(0, \frac{\pi}{2}\right)$.
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