If a graph is continuous is it differentiable? Why or Why not? Give examples to support your conclusion. If a graph is differentiable is it continuous? Why or Why not? Give examples to support your conclusion.
+If a graph is continuous, then it is not always differentiable. Example: If a function has derivatives from both the right and the left at a point. For this particular problem there would be no solution because it is not differentiable.
+If a graph is differentiable, then it is continuous. The only way the graph can be continuous is if it does not have any of the the four types of discontinuities. Example: So for example, if the function results in any jumps, removables, infinates, or oscillations the it would not be continuous.
-If a graph is continuous then it is not always differentiable.
Ex. If there is an absolute value then there will be a corner and you can not take the derivative of a corner but the graph is still continuous. This is why a graph can be continuous but not always differentiable.
-If a graph is differentiable then it is continuous.
When a graph has a jump, removable, infinate, or an oscillation then it is not continuous.
Ex. If the graph has any of these four discontinuities it is not differentiable and it is not continuous.
- If a graph is differentiable it is always continuous. This is because a graph can only be continuous if there are none of the four types of discontinuities in it. This means that the graph has no jumps or removables or vertical asymptotes or oscillations in it. Example: In the equation /x + 2/ the graph will have a corner, which means that derivatives do not exist. This means that the line is continuous ( because it does not have any of the different types of discontinuities in it ) and it is differentiable because it you can’t take a derivative of it. - If a graph is continuous, however, it is not always differentiable. Example: In the equation x – 2 there is a horizontal line at x = 2 so it is continuous because it does not have any of the different types of discontinuities but it is not differential.
If a graph is continuous, then it is not always differentiable. This is because a graph can only be continuous if there are none of the four types of discontinuities in it. This means that the graph has no jumps or removables or vertical asymptotes or oscillations in it. If there is an absolute value then there will be a corner and you can not take the derivative of a corner but the graph is still continuous. This is why a graph can be continuous but not always differentiable. - If a graph is continuous, however, it is not always differentiable. I'll address continuity from a graphical standpoint first. A function is continuous if you can sketch the entire graph without lifting your pencil from the paper. In other words, the graph has no breaks in it. One example is the graph of a parabola, f(x) = x^2 + 1. The graph for this function is continuous because you can plot a y-value for every possible x-value, and the y-values have no sudden jumps, so the graph is a smooth continuous graph.
If a graph is continuous, then it is not always differentiable. If a function has derivatives from both the right and the left at a point it doesn't mean there will always have a solution. If a graph is differentiable, then it is continuous. The only way the graph can be continuous is if it does not have any of the four types of discontinuities. So if it has any jumps, removable, infinities, or oscillations would not be continuous. An example of how an equation would be continuous is: In the equation x – 2 there is a horizontal line at x = 2 so it is continuous because it does not have any of the different types of discontinuities but it is not differential. An example of how you can’t find the derivative of an equation would be: In the equation /x + 2/ the graph will have a corner, which means that derivatives do not exist. This means that the line is continuous because it does not have any of the different types of discontinuities in it and it is differentiable because it you can’t take a derivative of it.
+If a graph is continuous, then it is not always differentiable.
ReplyDeleteExample:
If a function has derivatives from both the right and the left at a point.
For this particular problem there would be no solution because it is not differentiable.
+If a graph is differentiable, then it is continuous. The only way the graph can be continuous is if it does not have any of the the four types of discontinuities.
Example:
So for example, if the function results in any jumps, removables, infinates, or oscillations the it would not be continuous.
-If a graph is continuous then it is not always differentiable.
ReplyDeleteEx. If there is an absolute value then there will be a corner and you can not take the derivative of a corner but the graph is still continuous. This is why a graph can be continuous but not always differentiable.
-If a graph is differentiable then it is continuous.
When a graph has a jump, removable, infinate, or an oscillation then it is not continuous.
Ex. If the graph has any of these four discontinuities it is not differentiable and it is not continuous.
- If a graph is differentiable it is always continuous. This is because a graph can only be continuous if there are none of the four types of discontinuities in it. This means that the graph has no jumps or removables or vertical asymptotes or oscillations in it.
ReplyDeleteExample: In the equation /x + 2/ the graph will have a corner, which means that derivatives do not exist. This means that the line is continuous ( because it does not have any of the different types of discontinuities in it ) and it is differentiable because it you can’t take a derivative of it.
- If a graph is continuous, however, it is not always differentiable.
Example: In the equation x – 2 there is a horizontal line at x = 2 so it is continuous because it does not have any of the different types of discontinuities but it is not differential.
If a graph is continuous, then it is not always differentiable.
ReplyDeleteThis is because a graph can only be continuous if there are none of the four types of discontinuities in it. This means that the graph has no jumps or removables or vertical asymptotes or oscillations in it.
If there is an absolute value then there will be a corner and you can not take the derivative of a corner but the graph is still continuous. This is why a graph can be continuous but not always differentiable.
- If a graph is continuous, however, it is not always differentiable.
I'll address continuity from a graphical standpoint first. A function
is continuous if you can sketch the entire graph without lifting your
pencil from the paper. In other words, the graph has no breaks in it.
One example is the graph of a parabola, f(x) = x^2 + 1. The graph for
this function is continuous because you can plot a y-value for every
possible x-value, and the y-values have no sudden jumps, so the
graph is a smooth continuous graph.
If a graph is continuous, then it is not always differentiable. If a function has derivatives from both the right and the left at a point it doesn't mean there will always have a solution. If a graph is differentiable, then it is continuous. The only way the graph can be continuous is if it does not have any of the four types of discontinuities. So if it has any jumps, removable, infinities, or oscillations would not be continuous. An example of how an equation would be continuous is: In the equation x – 2 there is a horizontal line at x = 2 so it is continuous because it does not have any of the different types of discontinuities but it is not differential. An example of how you can’t find the derivative of an equation would be: In the equation /x + 2/ the graph will have a corner, which means that derivatives do not exist. This means that the line is continuous because it does not have any of the different types of discontinuities in it and it is differentiable because it you can’t take a derivative of it.
ReplyDelete