Download App

STD 12 - 6. Application of derivatives — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 6. Application of derivatives4 Marks
MCQ
In which interval $f(x) = 2x^2 - \ln |x| ,$  $(x \ne 0)$ is monotonically decreasing -
  • A
    $(-1/2 , 1/2)$
  • B
    $(- \infty , -1/2)$
  • ✓
    $( - \infty , - 1/2)\, \cup \,(0,1/2)$
  • D
    $( - \infty , - 1/2)\, \cup \,(1/2,\,\infty )$
✓

Answer

Correct option: C.
$( - \infty , - 1/2)\, \cup \,(0,1/2)$
c
$f(x)=2 x^{2}-\ln |x|$

$f^{1}(x)=4 x-\frac{1}{x}<0$

$\Longrightarrow x\left(x-\frac{1}{2}\right)\left(x+\frac{1}{2}\right)<0 \Longrightarrow x \in\left(-\infty,-\frac{1}{2}\right) \cup\left(0, \frac{1}{2}\right)$

$\ln (2), f(x)$ is monotonically decreasing

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The length of the perpendicular drawn from origin upon the straight line $\frac{x}{3} - \frac{y}{4} = 1$is
→
If $\int {\frac{{2{x^2} + 3}}{{({x^2} - 1)\,\,({x^2} + 4)}}dx = a\log \left( {\frac{{x - 1}}{{x + 1}}} \right) + } \,b{\tan ^{ - 1}}\frac{x}{2} + c$, then values of $a$ and $b$ are
→
Let the line passing through the points $(-1,2,1)$ and parallel to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4}$ intersect the line $\frac{x+2}{3}=\frac{y-3}{2}=\frac{z-4}{1}$ at the point $P$. Then the distance of P from the point $\mathrm{Q}(4,-5,1)$ is :
→
Let $\left\{a_{n}\right\}_{n=0}^{\infty}$ be a sequence such that $a _{0}= a _{1}=0$ and $a _{ n +2}=2 a _{ n +1}- a _{ n }+1$ for all $n \geq 0$. Then, $\sum\limits_{ n =2}^{\infty} \frac{ a _{ n }}{7^{ n }}$ is equal to
→
The term independent of $x$ in the expansion of $\left( {\frac{1}{{60}} - \frac{{{x^8}}}{{81}}} \right).{\left( {2{x^2} - \frac{3}{{{x^2}}}} \right)^6}$ is equal to
→
Let the coefficients of the middle terms in the expansion of $\left(\frac{1}{\sqrt{6}}+\beta x\right)^{4},(1-3 \beta x)^{2}$ and $\left(1-\frac{\beta}{2} x\right)^{6}, \beta>0$, respectively form the first three terms of an $A.P.$ If $d$ is the common difference of this $A.P.$, then $50-\frac{2 d}{\beta^{2}}$ is equal to.
→
The ${n^{th}}$ term of an $A.P.$ is $3n - 1$.Choose from the following the sum of its first five terms
→
If $f(x) = \left[ \begin{gathered}
  {e^x} + a\,\,\,for\,\,\,x\, < \,0 \hfill \\
  x - 3\,\,\,\,\,for\,\,\,x\, \geqslant \,0 \hfill \\ 
\end{gathered}  \right.\,,\,$ is differentiable at $x = 0$ , then $'a'$ equals to 
→
If $A$ and $B$ are two events such that $P(A \cap B)=0.1$, and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12 x^2-7 x+1=0$, then the value of $\frac{ P (\overline{ A } \cup \overline{ B })}{ P (\overline{ A } \cap \overline{ B })}$ is:
→
A point $\mathrm{z}$ moves in the complex plane such that $\arg \left(\frac{\mathrm{z}-2}{\mathrm{z}+2}\right)=\frac{\pi}{4}$, then the minimum value of $|z-9 \sqrt{2}-2 i|^{2}$ is equal to ..... .
→