# How is the function differentiable in graph?

If the graph of the function is a continuous line then the function is differentiable.

Also if the graph suddenly make a deviation at any point then the function is not differentiable at that point .

The slope of a tangent at any point of the graph gives the derivative of the function at that point.

### Condition for the continuity and differentiablity of a function?

An intuitive answer (NOTE: this is far from precise!) A function is continuous if you can trace its graph without lifting your pencil from the page. If, additionally, it is smooth everywhere without any jagged edges or abrupt corners, then it is differentiable. It is not possible for a function to be differentiable but not continuous. On the other hand, plenty of functions are continuous without being differentiable.

### When was function not having a derivative at a point?

Definition: A function f is differentiable at a if f'(a) exists. it is differentiable on an open interval (a, b) [or (a, ∞) or (-∞, a) or (-∞, ∞)]if it is differentiable at every number in the interval. Example: Where is the function f(x) = |x| differentiable? Answer: 1. f is differentiable for any x > 0 and x < 0. 2. f is not differentiable at x = 0. That's mean that the curve…

### Is signum function differentiable?

The signum function is differentiable with derivative 0 everywhere except at 0, where it is not differentiable in the ordinary sense. However, but under the generalised notion of differentiation in distribution theory, the derivative of the signum function is two times the Dirac delta function or twice the unit impulse function.

### When you say a function is not differentiable?

Well, firstly, the derivative of a function simply refers to slope. Usually we say that the function is not differentiable at a point. Say you have a function such as this: f(x)=|x| Another way to represent that would be as a piece-wise function: g(x) = { -x for x<0 { x for x>= 0 The problem arises at the specific point x=0. If you look at the slope--the change in the function--from the left and…

### Definition of Differentiable function?

Let f be a function with domain D in R, the real numbers, and D is an open set in R. Then the derivative of f at the point c is defined as: f'(c) =lim as x-> c of the difference quotient [f(x)-f(c)]/[x-c] If that limit exits, the function is called differentiable at c. If f is differentiable at every point in D then f is called differentiable in D.

### How do you get the tangent line without the graph?

The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.