Differentiable Function

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A Differentiable Function is a real-valued vector function that has a derivative function.



References

2012

  • (Wikipedia, 2012) ⇒ http://en.wikipedia.org/wiki/Differentiable_function
    • QUOTE: In calculus (a branch of mathematics), a differentiable function is a function whose derivative exists at each point in its domain. The graph of a differentiable function must have a non-vertical tangent line at each point in its domain. As a result, the graph of a differentiable function must be relatively smooth, and cannot contain any breaks, bends, or cusps, or any points with a vertical tangent.

      More generally, if x0 is a point in the domain of a function ƒ, then ƒ is said to be differentiable at x0 if the derivative ƒ′(x0) is defined. This means that the graph of ƒ has a non-vertical tangent line at the point (x0, ƒ(x0)), and therefore cannot have a break, bend, or cusp at this point.