From Math Images
|A Differentiable Function|
Basic DescriptionIf we were to draw a tangent through every point on the curve in the main image, we would not ecounter any difficulty at any point because there are no discontinuities, sharp corners and straight vertical portions at any point. This means that the function is differentiable.
A More Mathematical Explanation
A function is differentiable at a point if it has a tangent at every point. That is, a function is di [...]
A function is differentiable at a point if it has a tangent at every point. That is, a function is differentiable at if the limit
It fails to be differentiable if:
- is not continuous at
- The graph has a sharp corner at
- The graph has a vertical tangent line
Note: While all differentiable functions are continuous, all continuous functions may not be differentiable.
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