Limits, Continuity and Differentiability Part 2

f(x)={

(x−3)(x+1)e(3x−2)2;	x>3
−(x−3)(x+1)e(3x−2)2;	−1≤x≤3
(x−3)(x+1)e(3x−2)2;	x<−1

At x=−1 , let LHD be α, then its clear that RHD be -α.
Similarly, at x = 3, if LHD is β, then RHD at x = 3 will be − β.
So, f(x) is not differentiable at x = − 1, x = 3
At, all other points f(x) will be differentiable.