Download App

6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
The function $f(x) = 2ln\,|x| -x|x|$ is increasing on the interval
  • ✓
    $(0,1)$
  • B
    $(0,\infty)$
  • C
    $(-1,1)$
  • D
    $(-1,0)$
✓

Answer

Correct option: A.
$(0,1)$
a
$f(x) = \left\{ {\begin{array}{*{20}{c}}
{2\ln x - {x^2}}&{{\rm{if}}}&{x > 0}\\
{2\ln \left( { - x} \right) + {x^2}}&{{\rm{if}}}&{x < 0}
\end{array}} \right.$

$\Rightarrow f^{\prime}(x)=\left\{\begin{array}{ll}{\frac{2}{x}-2 x} & {\text { if } x>0} \\ {\frac{2}{x}+2 x} & {\text { if } x<0}\end{array}\right.$

$\therefore f^{\prime}(x)>0$ only for $x \in(0,1)$

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 6. Application of derivatives→6. 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

Which of the following is not true about feasibility?
→
If $f(x)$ = $\left\{ \begin{gathered}
  \frac{{a + 3\cos x}}{{{x^2}}},\,\,\,\,\,\,\,\,\,x < 0 \hfill \\
  b\,\tan \left( {\frac{\pi }{{\left[ {x + 3} \right]}}} \right),\,x \geqslant 0 \hfill \\ 
\end{gathered}  \right.$ is continuous at $x = 0$ , then
→
If the vectors $\vec{a}=\hat{i}+3 \hat{j}+\hat{k}, \vec{b}=2 \hat{i}-\hat{j}-\hat{k} $ and $\vec{c}=\lambda \hat{i}+7 \hat{j}+3 \hat{k}$ are coplanar then $\lambda=$ _________.
→
Suppose $X$ follows a binomial distribution with parameters $n$ and $p$, where $0 < p < 1.$ If $\frac{{P\,(X = r)}}{{P\,(X = n - r)}}$ is independent of $n$ and $r$, then
→
Given the inverse trigonometric function assumes principal values only. Let $\mathrm{x}, \mathrm{y}$ be any two real numbers in $[-1,1]$ such that $\cos ^{-1} \mathrm{x}-\sin ^{-1} \mathrm{y}=\alpha, \frac{-\pi}{2} \leq \alpha \leq \pi \text {. }$ Then, the minimum value of $x^2+y^2+2 x y \sin \alpha$ is
→
For square matrix A if $A = B +\frac{ C }{2}$, where B is skew symmetric matrix and C is symmetric matrix, then C = _________.
→
Which of the following is not correct?
  1. $|\text{A}|=|\text{A}^{\text{T}}|,$ where $\text{A}=[\text{a}_{\text{ij}}]_{3\times3}$
  2. $|\text{kA}|=|\text{k}^3|,$ where $\text{A}=[\text{a}_{\text{ij}}]_{3\times3}$
  3. If a is a skew-symmetric of odd order, then |A| = 0
  4. $\begin{vmatrix}\text{a}&\text{c}\\\text{e}&\text{g} \end{vmatrix}+\begin{vmatrix}\text{b}&\text{c}\\\text{f}&\text{g} \end{vmatrix}+\begin{vmatrix}\text{a}&\text{d}\\\text{e}&\text{h}\end{vmatrix}+\begin{vmatrix}\text{b}&\text{d}\\\text{f}&\text{h}\end{vmatrix}$
→
$\int\limits^\sqrt{3}_1\frac{1}{1+\text{x}^2}\text{ dx}$ is equal to:

  1. $\frac{\pi}{12}$

  2. $\frac{\pi}{6}$

  3. $\frac{\pi}{4}$

  4. $\frac{\pi}{3}$

→
${d \over {dx}}\left[ {\log \left( {x + {1 \over x}} \right)} \right] = $
→
If $\cos \left ( 2\sin^{-1}\text{x} \right )=\frac{1}{9}$​, the value of x which satify equation is $ \pm \frac{a}{b}$​. Find the value of a + b:
  1. 2
  2. 3
  3. 4
  4. 5
→