
What are some examples of non-differentiable functions?
Answer
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Hint: A function is said to be differentiable, if the derivative of the function exists at every point in its given domain. Geometrically the derivative of a function at a point is defined as the slope of the graph of at . Then the function is said to be non-differentiable if the derivative does not exist at any one point of its domain.
Complete step-by-step answer:
Some examples of non-differentiable functions are:
A function is non-differentiable when there is a cusp or a corner point in its graph. For example consider the function , it has a cusp at hence it is not differentiable at .
If the function is not continuous then it is not differentiable, i.e. when there is a gap or a jump in the graph of the function then it is not continuous hence not differentiable. For example consider the step function , here there is a jump discontinuity .
If the function can be defined but its derivative is infinite at a point then it becomes non-differentiable. This happens when there is a vertical tangent line at that point. For example, consider , it has a vertical tangent line at , therefore at its derivative is infinite.
When the function is unbounded and goes to infinity at some point of its domain it becomes non-differentiable. For example consider which goes to infinity at , hence non- differentiable
Note: If a function is differentiable then it is always continuous but the converse need not be true, i.e. there are functions which are continuous but not differentiable for example is continuous at but not differentiable at . By studying the graph of the given function we can easily conclude about the continuity and differentiability of the function.
Complete step-by-step answer:
Some examples of non-differentiable functions are:
A function is non-differentiable when there is a cusp or a corner point in its graph. For example consider the function

If the function is not continuous then it is not differentiable, i.e. when there is a gap or a jump in the graph of the function then it is not continuous hence not differentiable. For example consider the step function

If the function can be defined but its derivative is infinite at a point then it becomes non-differentiable. This happens when there is a vertical tangent line at that point. For example, consider

When the function is unbounded and goes to infinity at some point of its domain it becomes non-differentiable. For example consider

Note: If a function is differentiable then it is always continuous but the converse need not be true, i.e. there are functions which are continuous but not differentiable for example
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