The function y=2 x^2- |x|, x 0 decreases when x - Vidyadip

MCQ

The function $y=2 x^2-\ln |x|, x \neq 0$ decreases when $x \in$

A
$(-1,1)$
B
$R-\left\{-\frac{1}{2}, \frac{1}{2}\right\}$
C
$\left(-\frac{1}{2}, 0\right) \cup\left(\frac{1}{2}, \infty\right)$
✓
$\left(-\infty,-\frac{1}{2}\right) \cup\left(0, \frac{1}{2}\right)$

✓

Answer

Correct option: D.

$\left(-\infty,-\frac{1}{2}\right) \cup\left(0, \frac{1}{2}\right)$

(d)

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

Radius of a circle is increasing uniformly at the rate of $3\,cm/\sec .$ The rate of increasing of area when radius is $10\,cm$, will be

Area of one region included between the $sine$ and $cosine$ curves is given by

If abscissa of vertex of parabola $y = a{x^2} + bx + c$ is $1\left( {a,b,c > 0} \right)$ and $f(x) = \int\limits_0^x {\left( {3a{x^2} + bx + c} \right)dx} $ is strictly increasing function $\forall \,\,\,x\, \in \,R$ , then maximum possible value of $\left[ {\frac{a}{c}} \right]$ is (where [.] denotes greatest integer function)

If $[x]$ denotes the greatest integer less than or equal to $x,$ then the value of the integral $\int_0^2 {{x^2}[x]\,dx} $ equals

If $\text{y}=\log\sqrt{\tan\text{x}},$ then the value of $\frac{\text{dy}}{\text{dx}}$ at $\text{x}=\frac{\pi}{4}$ is givne by:

Two cards are drawn successively with replacement from a well shuffled deck of $52$ cards. Let $X$ denote the random variable of number of aces obtained in the two drawn cards. Then $P\,\left( {X = 1} \right)\, + P\,\left( {X = 2} \right)$ equals

If $A=\left[a_{i j}\right]$ is a square matrix of order 2 such that $a_{i j}=\left\{\begin{array}{ll}1, & \text { when } i \neq j \\ 0, & \text { when } i=j\end{array}\right.$ then $A^2$ is

The sum of the squares of sine of the angles made by the line $AB$ with $\text{OX, OY, OZ}$ where $O$ is the origin is:

If for the function $f(x) = \frac{1}{4}{x^2} + bx + 10$ ; $f\left( {12 - x} \right) = f\left( x \right)\,\forall \,x\, \in \,R$ , then the value of $'b'$ is

Choose the correct answer from the given four options: he two curves $x^3-3 x y^2+2=0$ and $3 x^2 y-y^3-2=0$ intersect at an angle of: