The function $f(x)=2 x^2-\log |x|$ is

decreasing in $\left(\frac{1}{2}, \infty\right)$

increasing in $\left(0, \frac{1}{2}\right)$

increasing in $\left(-\infty,-\frac{1}{2}\right)$

JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

The function

f(x)=2 x^2-\log |x|

View answer and explanation

Correct option: B

decreasing in

\left(0, \frac{1}{2}\right)

Option B is correct because the function's derivative is negative in the interval (0, 1/2), indicating a decreasing function.

Practice All Chapter MCQs →

f\left( x \right) = \frac{{K\sin x + 2\cos x}}{{\sin x + \cos x}}

x

f\left( x \right) = {x^2} + ax + 1

a

f(x)=

\sin x-\cos x-a x+b

f(x)=x e^{x(1-x)}, x \in R

f

g

fog

f\left( x \right) = {x^3} + b{x^2} + cx + d

0 < {b^2} < c

\left( { - \infty ,\;\infty } \right)