IIT JEE 1983 - 'Adapted' - FIB to MCQ Question 26

Calculus Level 5

The function f ( x ) = 2 x 2 ln x f(x)=2x^2-\ln |x| is monotonically increasing and monotonically decreasing for values of x 0 x\neq0 in the interval __________ \text{\_\_\_\_\_\_\_\_\_\_} and __________ \text{\_\_\_\_\_\_\_\_\_\_} , respectively.

Choose the most precise answer.


In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives .
( 1 2 , 0 ) ( 1 2 , ) (-\frac 12, 0)\cup(\frac 12, \infty) and ( , 1 2 ) ( 0 , 1 2 ) (-\infty, -\frac 12)\cup(0, \frac 12) ( 1 2 , 0 ) ( 1 2 , ) (-\frac 12, 0)\cup(\frac 12, \infty) and ( , 1 2 ] ( 0 , 1 2 ] (-\infty, -\frac 12]\cup(0, \frac 12] [ 1 2 , 0 ) [ 1 2 , ) [-\frac 12, 0)\cup[\frac 12, \infty) and ( , 1 2 ) ( 0 , 1 2 ) (-\infty, -\frac 12)\cup(0, \frac 12) All of the other options are correct

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