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|x+2| is continuous everywhere.
for case a,|x+2| is differentiable on (-2,4),whereas for case b,|x+2| is not differentiable on (-3,4) at x=-2..
also the slope of the tangent at every point to the given curve between (-2,0) is 1,which is the same as that of the chord joining the points (-2,0) and (4,6)..
thus all values of x between (-2,4) satisfy lagrange's theorem.