Non Differentiable Function

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 fx x , it has a

NOTE Although functions f, g and k whose graphs are shown above are continuous everywhere, they are not differentiable at 92 x 0 92. Examples with Solutions Analytical Proofs of non differentiability. Example 1 Show analytically that function f defined below is non differentiable at 92 x 0 92.

Non-differentiable functions often exhibit specific characteristics that set them apart from their differentiable counterparts. For instance, a common feature is the presence of sharp points or cusps, where the function abruptly changes direction. Additionally, these functions may have vertical tangents, which indicate that the slope approaches

Generally the most common forms of non-differentiable behavior involve a function going to infinity at x, or having a jump or cusp at x. There are however stranger things. The function sin1x, for example is singular at x 0 even though it always lies between -1 and 1. Continuous but non differentiable functions . Up

2.4 Graphs of Functions 2.5 Vertical Line Test 2.6 Domain and Range Using Graph 2.7 Piecewise-Defined Functions 2.8 Equal Functions 2.9 Even and Odd Functions 2.10 Examples of Elementary Functions 2.11 Transformations of Functions 2.12 Algebraic Combination of Functions 2.13 Composition of Functions 2.14 Increasing or Decreasing Functions

For functions of more than one variable, differentiability at a point is not equivalent to the existence of the partial derivatives at the point there are examples of non-differentiable functions that have partial derivatives. For example, the function

the product of two convex functions is not a convex function in general. For instance, 92fx x92 and 92gx x292 are convex functions, but 92hxx392 is not a convex function. The following result may be considered as a version of the first derivative test for extrema in the case of non differentiable functions.

Learn the definition and examples of differentiable, continuously differentiable, infinitely differentiable, and non differentiable functions. Find out how to check for corners, cusps, vertical tangents, and jump discontinuities in graphs.

What are non differentiable points. In the entry on derivatives, we saw that if a function 92 fx 92 is differentiable at a point 92 c 92, then the function is continuous at that point. However, there are cases where a function is continuous at 92 c 92 but not differentiable. More generally, the non-differentiable points of a function 92 fx 92 occur when

Learn why differentiation cannot be applied to some functions, such as those with jumps, kinks, vertical tangents, or infinite values. See examples of non-differentiable functions and their graphs, and how to identify them.