? ::Thus at A tangent is not defined... 
Hence the function is not differentiable at A

Non Differentiable Function-A visualiasation

a project by
Benny Varghese
Ashly Villa
Thrissur-680014

By moving the slider , make tanget at A

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How to Proceed ?
Using sliders on the Left ,TRY to bring tangents 
(Red and Blue Lines) at A. We see that there is no 
tangent possible  at A showing that function is 
Not differentiable at A and hence its not  differentiable

f(x) = ((x - 4) * abs(x - 4)) + 2.5
g(x) = (x - 7)^(2) + 2.5
A = Intersect(g, f, (5.5, 4.75))
h(x) = If[x ≤ 5.5, f, g]
a = 3.13 (slider from 3 to 5.5, step 0.01)
B: (a, h(a))
b = Tangent(B, h)
c = 7.44 (slider from 5.51 to 10, step 0.01)
C: (c, h(c))
d = Tangent(C, h)