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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.
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What function is continuous everywhere but not differentiable?
Weistrass function is continuous everywhere but not differentiable everywhere
Is there a function that is continuous everywhere differentiable at rationals but not differentiable at irrationals?
No.
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 y = |x| has not a tangent at (0, 0).Thus, both continiuty and differentiability are desirable properties for a function to have. These properties are related.Theorem: If f is differentiable at a, then f is continuous at a.The converse theorem is false, that is, there are functions that are continuous but not differentiable. (As we saw at the example above. f(x) = |x| is contionuous at 0, but is not differentiable at 0).The three ways for f not to be differentiable at aare:a) if the graph of a function f has a "corner" or a "kink" in it,b) a discontinuity,c) a vertical tangent
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.
Where is f(x) discontinuous but not differentiable Explain?
Wherever a function is differentiable, it must also be continuous. The opposite is not true, however. For example, the absolute value function, f(x) =|x|, is not differentiable at x=0 even though it is continuous everywhere.
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 analitic?
which function is not differentiable infinitely many time.
What are the similarities between quadratic function and linear function?
Both are polynomials. They are continuous and are differentiable.
What is differentiability in math?
A function is differentiable at a point if the derivative exists there.
How do you find the vertices of a cubic function?
A cubic function is a smooth function (differentiable everywhere). It has no vertices anywhere.
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= 0The problem arises at the specific point x=0. If you look at the slope--the change in the function--from the left and right of x, you notice that it is different, negative 1 and positive 1. So, we can say that the function is not differentiable at x=0 because of that sudden change.There are however, a few functions that are nowhere differentiable. One example is the Weirstrass function. The even more ironic thing about this function is that it is continuous everywhere! Since this function is not differentiable anywhere, many might call it a non-differentiable function.There are absolutely other examples.
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.
