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#TestDifferentiability
Continuity
The function f is continuous at x=c iff f(c) exists
lim┬(x→c)⁡〖f(x)〗 exists
lim┬(x→c)⁡〖f(x)〗=f(c)
Differentiability
The function f is differentiable at x=c if f'(c) has a numeric value
If f is differentiable at every value of x in an interval, then f is differentiable on that interval.
NOTE: The limits of f'(c) should exist for differentiability