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L e tf(x)={x+2,x<-1x^2,-1lt=x<1(x-2)^2,x...

`L e tf(x)={x+2,x<-1x^2,-1lt=x<1(x-2)^2,xgeq1` Then number of times `f^(prime)(x)` changes its sign in `(-oo,oo)` is___

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The correct Answer is:
4
`f(x)={{:(1,xlt-1),(2x,-1ltxlt1),(2(x-2),xgt1):}`
f(x) changes sign at x =-1,0,1,2
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