Download App

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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
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

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

Let $f:\left[ { - 2,3} \right] \to \left[ {0,\infty } \right)$ be a continuous function such that $f(1-x) = f(x)$ for all $x \in \left[ { - 2,3} \right]$ . If $R_1$ is the numerical value of the area of the region bounded by $y =f (x), x = -2, x = 3$ and the axis of $x$ and ${R_2} = \int\limits_{ - 2}^3 {x\,f\left( x \right)} dx$ , then
→
Choose the correct answer from the given four options.
If $\text{P}(\text{A})=\frac{4}{5},$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{10},$ then $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)$ is equal to:
→
Distance of the point $(\alpha, \beta, \gamma)$ from $y$-axis is
→
If $a, b$  and  $c$  be three non-zero vectors, no two of which are collinear. If the vector $a + 2b$ is collinear with $ c$  and $b + 3c$ is collinear with a, then ($\lambda $ being some non-zero scalar) $a + 2b + 6c$ is equal to
→
Evaluate: $\int[\sin (\log x)+\cos (\log x)] d x$
→
 The area bounded by y –1 = |x|, y = 0 and |x|  $=\frac{1}{2}$  will be:
  1. $\frac{3}{4}$
  2. $\frac{3}{2}$
  3. $\frac{5}{4}$
  4. $\text{None of these}$
→
Magnitudes of vectors $ \vec a,\vec b,\vec c$ are $3,4,5 $ respectively. If $\vec a$ and $ \vec b+\vec c, \vec b$ and $\vec c+ \vec a,\vec c $ and $\vec a + \vec b$ are mutually perpendicular, then magnitude of $|\vec a + \vec b + \vec c|$
→
The area of the region bounded by the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ is _________ sq. unit.
→
If the system of linear equations  $x_1 + 2x_2 + 3x_3 = 6$ ; $x_1 + 3x_2 + 5x_3 = 9$ ; $2x_1 + 5x_2 + ax_3 = b$ is consistent and has infinite number of solutions, then
→
$\int_{}^{} {{x^n}\log x\;dx = } $
→