Find the maximas and minimas in |1/(2|x|-1)-2|.Please draw the graph.

the approch to solve this question is to find out the values which x can't take and divide the real line into intervals in which x exists and then use differentiation to find maxima and minima.also check the value of the expresion at the boundary of the intervals including the positive and negative infinities if x can tend them.

the minima is 0, and maxima does nt exist as it tends to infinity(positive,obviously!!).

graph can be drawn easily by analysing the intervals of x explained above  ,taking special care to the boundary values.