Number of points where `f(x)=x^2-|x^2-1|+2||x|-1|+2|x|-7` is non-differentiable is

Options

A. 0
B. 1
C. 2
D. 3

Answer

A

Explanation

Clearly f(x) is continuous for all real x.
`f(x)=x^(2)-|x^(2)-1|+2||x|-1|+2|x|-7`
`={{:(x^(2)-(x^(2)-1)+2(-x-1)-2x-7",",xlt-1),(x^(2)-(1-x^(2))+2(x+1)-2x-7",",-1lexle0),(x^(2)-(1-x^(2))+2(1-x)+2x-7",",0lexlt1),(x^(2)-(x^(2)-1)+2(x-1)+2x-7",",xgt1):}`
`{{:(-4x-8",",xlt-1),(2x^(2)-6",",-1lexlt0),(2x^(2)-6",",0lex lt1),(4x-8",",xgt1):}`
`f'(x)={{:(-4",",xlt-1),(4x",",-1ltxlt0),(4x",",0ltxlt1),(4",",xgt1):}`
Clearly, f(x) is differentiable for all real x.