Let `I RvecI R` be defined as `f(x)=|x|++x^2-1|dot` The total number of points at which `f` attains either a local maximum or a local minimum is_______

Answer

5

Explanation

`f(x)=|x|+|x^(2)-1|`
`f(X)=(x)/(x)+(x^(2)-1)/(x^(2)-1).(2x)={{:(2x-1,xlt-1),((2x+1),-1ltxlt0),(1-2x,0ltxlt1),(2x+1,xgt1):}`

So f(x) changes sign at points x=-`1,-1//2,1//2,0,1//2,,1`
so total number of points of local maximum or minimum is 5