Differentiability and Continuity

Data Science, AI and ML
#1

For example 3, the function h(x) = 1/x is undefined at the point x=0. Hence, its derivative (-1/x^2) is also not defined at x=0. If a function is not continuous at a point, then it does not have a derivative at that point. Below are a few scenarios, where a function is not differentiable:

  1. If the function is not defined at a point
  2. Function does not have a limit at that point
  3. If the function is not continuous at a point
  4. The function has a sudden jump at a point

Following are a few examples:

Examples of Points at Which there is no Derivative

Examples of Points at Which there is no Derivative

Extensions

This section lists some ideas for extending the tutorial that you may wish to explore.

  • Velocity and instantaneous rates of change
  • Rules for derivatives
  • Integration