What is a differentiable function?
If the function f(x) is differentiable at x = a, it means f(x) can be approximated by a linear function that passes through the point (a, f(a)):
f(x) = f(a) + m(x-a) + o(|x-a|)
where m = df(a)/dx is the slope and o(|x-a|) (little-o) is the error term.
As x goes to a, f(x) converges to f(a). Hence, if f(x) is differentiable, it is also continuous.
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