0
Can a graph be differentiable at a specific point but not continuous at the same point?
Not according to the usual definitions of "differentiable" and "continuous".
Suppose that the function f is differentiable at the point x = a.
Then f(a) is defined and
limit (h -> 0) [f(a+h) - f(a)]/h exists (has a finite value).
If this limit exists, then it follows that
limit (h -> 0) [f(a+h) - f(a)] exists and equals 0.
Hence limit (h -> 0) f(a+h) exists and equals f(a).
Therefore f is continuous at x = a.
What else can I help you with?
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.
Can a non continuous function be differentiable?
No, a non-continuous function cannot be differentiable at the points of discontinuity. Differentiability requires the existence of a well-defined tangent line at a point, which necessitates continuity at that point. However, a function can be differentiable on intervals where it is continuous, even if it has discontinuities elsewhere.
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.
What is point 00 on a graph is called?
The Origin
What can be used to determine if a graph represents a function?
If the graph is a function, no line perpendicular to the X-axis can intersect the graph at more than one point.
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.
Can a non continuous function be differentiable?
No, a non-continuous function cannot be differentiable at the points of discontinuity. Differentiability requires the existence of a well-defined tangent line at a point, which necessitates continuity at that point. However, a function can be differentiable on intervals where it is continuous, even if it has discontinuities elsewhere.
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
When finding the derivative of a point on a piecewise function does every function in the piecewise function need to be continuous and approach the same limit?
All differentiable functions need be continuous at least.
What term is a graph of isolated points?
A graph of isolated points is typically referred to as a "discrete graph." In such a graph, each point represents an individual data value or a specific coordinate, and there are no continuous connections between them. This contrasts with continuous graphs, where points are connected to form lines or curves. Discrete graphs are often used to represent datasets where values are distinct and separate, such as in certain types of statistical data or functions defined only at specific intervals.
Does the derivative function exist for all values of x?
The existence of a derivative function at a given point depends on the behavior of the original function at that point. A derivative exists at a point if the function is continuous and has a defined slope (i.e., is differentiable) at that point. However, there are functions that are not differentiable at certain points—such as those with sharp corners, vertical tangents, or discontinuities—meaning the derivative does not exist for all values of ( x ). Thus, while many functions are differentiable everywhere, not all functions possess derivatives across their entire domain.
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.
What is differentiability in math?
A function is differentiable at a point if the derivative exists there.
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.
What is a graph of isolated points called?
A graph of isolated points is called a discrete graph. In this type of graph, each point represents a distinct value or data point, and there are no connections or edges between them, highlighting their individual significance. Discrete graphs are often used to represent data sets where values are separate and not continuous.
Name What graph has a finite or limited number of data?
A graph that has a finite or limited number of data points is typically referred to as a discrete graph. Discrete graphs represent data that can take on specific, separate values, often illustrated with distinct points rather than continuous lines. Examples include bar graphs and scatter plots, where each point correlates to a specific data value.
