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APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES1 Mark
MCQ
Choose the correct answer from the given four options:
Which of the following functions is decreasing on $\Big(0,\frac{\pi}{2}\Big)?$
  • A
    $\sin2\text{x}$
  • B
    $\tan\text{x}$
  • ✓
    $\cos\text{x}$
  • D
    $\cos3\text{x}$
✓

Answer

Correct option: C.
$\cos\text{x}$
$​​\text{f}_1(\text{x})=\sin2\text{x},$ increases from '0' to '1' in $\Big(0,\frac{\pi}{2}\Big)$
$\text{f}_2(\text{x})=\tan\text{x}$ is increasing function in each quadrant.
$\text{f}_3(\text{x})=\cos\text{x},$ decreases from '1' to '0' in $\Big(0,\frac{\pi}{2}\Big) $
$ \text{f}_4(\text{x})=\cos3\text{x},$ decreases if $3\text{x}\in\Big(0,\frac{\pi}{2}\Big)\ \text{or x }\in\Big(0,\frac{\pi}{6}\Big)$

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