00:01
So, a function f of x is differentiable if first, its derivative of function exists, that is the derivative of the function exists every point in its given domain.
00:37
Also, geometrically, the derivative of function f of x is at point x equal to x0 is defined as the slope of the graph of f of x at x equal to x0.
00:58
So, then the function is said to be differentiable.
01:04
So, similarly, f of x is a function is not differentiable if the derivative does not exist.
01:21
Derivative does not exist at any one point of its domain.
01:42
Geometrically seeing a function is differentiable or not, so only when its derivative at some point x equal to x0, the slope is present, so the slope is defined as the derivative.
01:54
Now we will see some examples of non -differentiable functions.
01:59
So if a non -differential function, there is a cusp or a corner, so we will see a function such that it is defined like this and its equation is f of x is equal to mod of x.
02:13
So, here we can see that there is a corner forming at x equal to 0.
02:20
Hence it is not differentiable at this point.
02:23
So, we can say that it is a non -differentiable function.
02:26
Similarly, if there is a function called as step function and its value is x over mod of x and its graph can be seen like this.
02:40
So, it breaks at this point and at this point.
02:46
So, at this point it is seen to be non -continuous.
02:51
Hence it is not differentiable...