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Let f : R rarr R be given by f(x) = {{:...

Let `f : R rarr R` be given by `f(x) = {{:(x^5+5x^4 +10x^3+10x^2+3x+1,xlt0),(" "x^2-x+1,0le x lt1),(" "2/3x^(3)-4x^2+7x-8/3,1lexlt3),(" "(x-2)log_(e)(x-2)-x+10/3,xge3):}`
Then which of the following options is/are correct?

A

f is increasing on `(-oo,0)`

B

f' has a local maximum at x = 1

C

f is onto

D

f' is NOT differentiable at x = 1

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