Download App

APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES1 Mark
MCQ
At $\text{x}=\frac{5\pi}{6}, $ $\text{f}(\text{x})=2\sin3\text{x}+3 \cos3\text{x}$ is:
  • A
    0
  • B
    maximum.
  • C
    minimum.
  • ✓
    none of these.
✓

Answer

Correct option: D.
none of these.
Given, $\text{f}(\text{x})=2\sin3\text{x}+3 \cos3\text{x}$
$\Rightarrow \text{f}'(\text{x})=6 \cos3\text{x}-9\cos3\text{x}$

to find maxima or minima f'(x) = 0

$6 \cos3\text{x}-9\cos3\text{x}=0$

$\Rightarrow \tan3\text{x}=\frac{2}{3}$

$\text{f}'\Big(\frac{5\pi}{6}\Big)=\tan\Big(3\times\frac{5\pi}{6}\Big)$

$\text{f}'\Big(\frac{5\pi}{6}\Big)=\tan\Big(\frac{5\pi}{2}\Big)$

$\Rightarrow\text{f}'\Big(\frac{5\pi}{6}\Big)=\tan\Big(2\pi+\frac{\pi}{2}\Big)$

$\Rightarrow\text{f}'\Big(\frac{5\pi}{6}\Big)=\tan\Big(\frac{\pi}{2}\Big)$ which is not defined.

Hence, $\text{x}=\frac{5\pi}{6}$ is not a critical point.

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 function $f(x) = x^3 - 9kx^2 + 27x + 30$ is increasing on $R,$ then:
→
Which of the following represents coinitial vector:
→
If vectors satisfy the condition $|a - c| = |b - c|$, then $(b - a)\,.\,\left( {c - \frac{{a + b}}{2}} \right)$ is equal to
→
The equations in terms of $x$ and $y$ are:
→
If $\text{y}=\sin(\text{m}\sin^{-1}\text{x}),$ then $(1-\text{x}^2)\text{y}_2-\text{xy}_1$ is equal to :
→
The solution of the differential equation $2\text{x}\frac{\text{dy}}{\text{dx}}-\text{y}=3$ resresents:
→
Among :

$( S 1): \lim _{ n \rightarrow \infty} \frac{1}{ n ^2}(2+4+6+\ldots \ldots \ldots+2 n)=1$

(S2) : $\lim _{ n \rightarrow \infty} \frac{1}{ n ^{16}}\left(1^{15}+2^{15}+3^{15}+\ldots \ldots \ldots .+ n ^{15}\right)=\frac{1}{16}$

→
The maximum value of the object function $Z = 5x + 10y$ subject to the constraints $\text{x}+2\text{y}\leq120,\text{x}+\text{y}\geq60,\text{x}-2\text{y}\geq0,\text{x}\geq0,\text{y}\geq0$ is:
→
The differential equation whose solution is $A{x^2} + B{y^2} = 1$ where $A$ and $B$ are arbitrary constants is of
→
The area bounded by $y –1 = |x|, y = 0$ and $|x| \frac{1}{2}$ will be:
→