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.
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.
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.
The Origin
If the graph is a function, no line perpendicular to the X-axis can intersect the graph at more than one point.
manipulated variable
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.
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.
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
All differentiable functions need be continuous at least.
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.
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.
A function is differentiable at a point if the derivative exists there.
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.
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.
To find acceleration from a speed-time graph, you need to calculate the slope of the speed-time graph. The slope at any point on the speed-time graph represents the acceleration at that specific time. If the speed-time graph is linear, then the acceleration will be constant. If the speed-time graph is curved, you can find the acceleration by calculating the slope of the tangent line at a specific point.
"Will be returning" is in the future continuous tense. It indicates an action that will be happening continuously at a specific point in the future.
You can find the speed of an object from its distance-time graph by calculating the slope of the graph at a specific point. The slope represents the object's velocity at that particular moment. By determining the slope, you can find the speed of the object at that point on the graph.