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approaches a [[limit]]ing value that we call the [[derivative]] of the function f(x) at ''x=a''.
approaches a [[limit]]ing value that we call the [[derivative]] of the function f(x) at ''x=a''.
There is also the more rigorous <math>\epsilon-\delta</math> definition: a function f is said to be differntiable at point ''a'' if ∀<math>\epsilon>0</math> ∃<math>\delta>0</math> such that if
::<math> |x - a| < \delta\,</math>
then
::<math>|\frac{f(x) - f(a)}{x-a} - f'(a) | < \epsilon \,</math>.
[[category:calculus]]
[[category:calculus]]