The function `y=2x^2-ln|x|` is monotonically increasing for values of `x(!=0)` satisfying the inequalities____ and monotonically decreasing for values of `x` satisfying the inequalities_____.

Answer

d

Explanation

Here, ` y = {{:(2x^(2)- logx",",, x gt 0 ), (2x ^(2) - log (-x)",",, x lt 0):}`
`rArr (dy )/(dx) = {{:( 4x - (1)/(x) ",",, x gt 0 ),(4x - (1)/(x)",",, x lt 0 ):}`
`" " = (4x^(2) - 1)/( x ), x in R - {0} -= (( 2 x - 1)( 2x + 1))/( x )`
`therefore ` Increasing when ` x in ((1)/(2), 0) uu ((1)/(2), oo)`
and decreasing when ` x in (-oo, - (1)/(2)) uu (0, (1)/(2) )`