f(x)= +3 is maximum when x = - Vidyadip

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.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Application of Derivatives→Application of Derivatives — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If the points $\left(x_1, y_1\right),\left(x_2, y_2\right)$ and $\left(x_1+x_2, y_1+y_2\right)$ are collinear, then $x_1 y_2$ is equal to

$A$ = $f(x)$ = $\left[ {\begin{array}{*{20}{c}}
{\cos x}&{\sin x}&0 \\
{ - \sin x}&{\cos x}&0 \\
0&0&1
\end{array}} \right]$ . Then $A^{-1}$ is equal to

The distance of the line $\vec{\text{r}}=2\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}+\lambda(\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}})$ from the plane $\vec{\text{r}}.(\hat{\text{i}}+5\hat{\text{j}}+\hat{\text{k}})=5$ is:

The equation $2\cos^{-1}\text{x}+\sin^{-1}\text{x}=\frac{11\pi}{6}$ has:

Let $A =$ $\left[ {\begin{array}{*{20}{c}}1&{\sin \theta }&1\\{ - \sin \theta }&1&{\sin \theta }\\{ - 1}&{ - \sin \theta }&1\end{array}} \right]$, where $0 \le \theta < 2\pi$ , then

If $x$ is real$,$ the minimum value of $x^2 - 8x + 17$ is:

Let $\mathrm{M}$ and $\mathrm{m}$ respectively be the maximum and minimum values of the function $f(x)=\tan ^{-1}(\sin x+\cos x)$ in $\left[0, \frac{\pi}{2}\right]$, Then the value of $\tan (\mathrm{M}-\mathrm{m})$ is equal to:

The value of $\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{j=1}^{n} \frac{(2 j-1)+8 n}{(2 j-1)+4 n}$ is equal to:

The function $f: R \rightarrow R$ defined by $f(x)=6^x+6^{|x|}$ is

If $f$ is twice differentiable such that $f''\,(x)\,\, = \,\, - \,f(x)\,,\,\,f'\,(x)\,\, = \,\,g(x)$ , $h'\,(x)\,\, = \,\,{{\left[ {f(x)} \right]}^2}\,\, + \,\,{{\left[ {g(x)} \right]}^2}\,\,\,$ and $h\,(0)\,\, = \,\,2\,,\,\,h\,(1)\,\, = \,\,4$ then the equation $y = h(x)$ represents :