Max Curvature Points on y=ex & xy=1 - Help Needed!

In summary, The conversation is about a person asking for help in finding the point or points on a curve where the curvature is at its maximum for two equations: y=ex and xy=1. The other person suggests using the formula for curvature and provides the formula. The person asking for help eventually figures out the solution and thanks the other person for their assistance.
  • #1
Giuseppe
42
0
Hello, I just learned how to do these types of problems, but I'm having trouble. Can some one direct me through this problem?

Find the point or points on the curve which the curvature is a maximum for

a. y=ex
b. xy=1

any help is greatly appreciated. I really am stuck here!
 
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  • #2
Giuseppe said:
Hello, I just learned how to do these types of problems, but I'm having trouble. Can some one direct me through this problem?

Find the point or points on the curve which the curvature is a maximum for

a. y=ex
b. xy=1

any help is greatly appreciated. I really am stuck here!

Is that ex or ex?

Do you know the formula for curvature? If so, find the curvature of each, then optimize it! If not, then that is what you should look up first :smile:

By the way, like I have mentioned a few times here:

[tex]\kappa=\frac{|\mathbf{r}'\times\mathbf{r}''|}{|\mathbf{r}'|^3}[/tex]

You can use r = (x)i + (ex)j for the first, and the second is similar (I think you can see what it will be).
 
Last edited:
  • #3
ah , i think i got it. thanks, i was being stupid
 

1. What is the equation for finding the maximum curvature points on y=ex?

The equation for finding the maximum curvature points on y=ex is given by:
Curvature = (2-e-x) / (1+e-x)3

2. How do you find the maximum curvature points on y=ex?

To find the maximum curvature points on y=ex, you can use the equation:
Curvature = (2-e-x) / (1+e-x)3
Set the derivative of the curvature equation to 0 and solve for x. The resulting values of x will be the maximum curvature points.

3. What is the equation for finding the maximum curvature points on xy=1?

The equation for finding the maximum curvature points on xy=1 is given by:
Curvature = (2xy2-y) / (x2+y2)3/2

4. How do you find the maximum curvature points on xy=1?

To find the maximum curvature points on xy=1, you can use the equation:
Curvature = (2xy2-y) / (x2+y2)3/2
Set the derivative of the curvature equation to 0 and solve for x and y. The resulting values of x and y will be the maximum curvature points.

5. Can you use the same method to find maximum curvature points for any function?

No, the method for finding maximum curvature points on y=ex and xy=1 is specific to those equations. Other equations may require different methods for finding maximum curvature points.

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