Discuss the extreama of the following functions
`(i)f(x)=|x|,(ii)f(x)=e^(-|x|),(iii) f(x)=x^(2//3)`

Explanation

f(x)=|x|

From the graph x=0 is point of minima as `f(x)ltf(x0-delta)` and `f(0)ltf(0+delta)(x)=e^(-|x|)`
`f(x)={e^(-x),xge0`
`e^(x),xlt0`

From the graph x=0 is point of maxima
(iii) f(x) =`x^(2//3)`
`f(x)=(2)/(3x^(1/3))`
Clearly f(0) does not exist as function has vertical tangent at x=0
`f(x)lt0` for `xlt0` and `f(x)gt0` for `xgt0`
f(x) has point of minima at x=0