Maxima and Minima — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsMaxima and Minima1 Mark
MCQ
$\text{f}(\text{x})=\sin +\sqrt{3}\cos\text{x}$ is maximum when x =
A
$\frac{\pi}{3}$
B
$\frac{\pi}{4}$
✓
$\frac{\pi}{6}$
D
$0$
✓
Answer
Correct option: C.
$\frac{\pi}{6}$
$\text{f}(\text{x})=\sin +\sqrt{3}\cos\text{x}$
$\Rightarrow\text{f}'(\text{x})=\cos\text{x}-\sqrt{3}\sin\text{x}$
For maxima or maxima,
f'(x) = 0
$\cos\text{x}-\sqrt{3}\sin\text{x}=0$
$\Rightarrow\ \tan\text{x}=\frac{1}{\sqrt{3}}\Rightarrow\text{x}=\frac{\pi}{6}$
$\text{f}''\Big(\frac{\pi}{6}\Big)=-\sin\frac{\pi}{6}-\sqrt{3}\cos\frac{\pi}{6}=\frac{-1-\sqrt{3}}{2}<0$
function has local maima at $\text{x}=\frac{\pi}{6}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.