Mixing
Area of circle showing concavity
1
$begingroup$
How to find the area of circle showing the change of concavities of function $$displaystyle f(x,y)=1-e^{-(x^2+y^2)/2}$$
multivariable-calculus
edited Jan 23 at 0:25
El borito
666216
asked Jan 23 at 0:19
Andy LamAndy Lam
63
$endgroup$
add a comment |
1
$begingroup$
How to find the area of circle showing the change of concavities of function $$displaystyle f(x,y)=1-e^{-(x^2+y^2)/2}$$
multivariable-calculus
edited Jan 23 at 0:25
El borito
666216
asked Jan 23 at 0:19
Andy LamAndy Lam
63
$endgroup$
1
$begingroup$
Which circle? What radio is it?
$endgroup$
– El borito
Jan 23 at 0:24
$begingroup$
the circle is inside the graph of the function
$endgroup$
– Andy Lam
Jan 23 at 0:27
add a comment |
1
1
1
$begingroup$
How to find the area of circle showing the change of concavities of function $$displaystyle f(x,y)=1-e^{-(x^2+y^2)/2}$$
multivariable-calculus
edited Jan 23 at 0:25
El borito
666216
asked Jan 23 at 0:19
Andy LamAndy Lam
63
$endgroup$
How to find the area of circle showing the change of concavities of function $$displaystyle f(x,y)=1-e^{-(x^2+y^2)/2}$$
multivariable-calculus
multivariable-calculus
edited Jan 23 at 0:25
El borito
666216
asked Jan 23 at 0:19
Andy LamAndy Lam
63
edited Jan 23 at 0:25
El borito
666216
asked Jan 23 at 0:19
Andy LamAndy Lam
63
edited Jan 23 at 0:25
El borito
666216
edited Jan 23 at 0:25
El borito
666216
edited Jan 23 at 0:25
El borito
666216
666216
asked Jan 23 at 0:19
Andy LamAndy Lam
63
asked Jan 23 at 0:19
Andy LamAndy Lam
63
asked Jan 23 at 0:19
Andy LamAndy Lam
63
63
1
$begingroup$
Which circle? What radio is it?
$endgroup$
– El borito
Jan 23 at 0:24
$begingroup$
the circle is inside the graph of the function
$endgroup$
– Andy Lam
Jan 23 at 0:27
add a comment |
1
$begingroup$
Which circle? What radio is it?
$endgroup$
– El borito
Jan 23 at 0:24
$begingroup$
the circle is inside the graph of the function
$endgroup$
– Andy Lam
Jan 23 at 0:27
1
1
$begingroup$
Which circle? What radio is it?
$endgroup$
– El borito
Jan 23 at 0:24
$begingroup$
Which circle? What radio is it?
$endgroup$
– El borito
Jan 23 at 0:24
$begingroup$
the circle is inside the graph of the function
$endgroup$
– Andy Lam
Jan 23 at 0:27
$begingroup$
the circle is inside the graph of the function
$endgroup$
– Andy Lam
Jan 23 at 0:27
add a comment |
1 Answer
1
active
oldest
votes
1
$begingroup$
The red circle shows where the curvature on the function changes sign. (Perhaps this is what the OP seeks... hard to know.)
Here's a cross section (in blue) and the second derivative (in tan), which changes sign at radius = 1.
answered Jan 23 at 0:30
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
$begingroup$
so it is impossible to find the area of circle?
$endgroup$
– Andy Lam
Jan 23 at 0:36
1
$begingroup$
Let me guess his circle is the boundary of the set of $(x,y)$ values for which the Hessian matrix is negative definite. And that his textbook or notebook has a non-standard definition of concavity.
$endgroup$
– kimchi lover
Jan 23 at 0:42
$begingroup$
that's right except I haven't learned about Hessian matrix so is there any way to find the that circle without using Hessian matrix?
$endgroup$
– Andy Lam
Jan 23 at 0:46
$begingroup$
@kimchilover: Given the level of sophistication of the OP (his reputation is $6$), I strongly doubt he's working with Hessians.
$endgroup$
– David G. Stork
Jan 23 at 0:46
$begingroup$
@AndyLam, maybe you should spell out exactly what "concavities of a function" means in your textbook or course? I think there is a terminology mismatch going on. To me, a function is concave on all of its range at once, or not; I'm afraid to you a function can be concave at particular points and not others. What is your official precise definition of "concave"?
$endgroup$
– kimchi lover
Jan 23 at 0:59
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
1
$begingroup$
The red circle shows where the curvature on the function changes sign. (Perhaps this is what the OP seeks... hard to know.)
Here's a cross section (in blue) and the second derivative (in tan), which changes sign at radius = 1.
answered Jan 23 at 0:30
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
$begingroup$
so it is impossible to find the area of circle?
$endgroup$
– Andy Lam
Jan 23 at 0:36
1
$begingroup$
Let me guess his circle is the boundary of the set of $(x,y)$ values for which the Hessian matrix is negative definite. And that his textbook or notebook has a non-standard definition of concavity.
$endgroup$
– kimchi lover
Jan 23 at 0:42
$begingroup$
that's right except I haven't learned about Hessian matrix so is there any way to find the that circle without using Hessian matrix?
$endgroup$
– Andy Lam
Jan 23 at 0:46
$begingroup$
@kimchilover: Given the level of sophistication of the OP (his reputation is $6$), I strongly doubt he's working with Hessians.
$endgroup$
– David G. Stork
Jan 23 at 0:46
$begingroup$
@AndyLam, maybe you should spell out exactly what "concavities of a function" means in your textbook or course? I think there is a terminology mismatch going on. To me, a function is concave on all of its range at once, or not; I'm afraid to you a function can be concave at particular points and not others. What is your official precise definition of "concave"?
$endgroup$
– kimchi lover
Jan 23 at 0:59
add a comment |
1
$begingroup$
The red circle shows where the curvature on the function changes sign. (Perhaps this is what the OP seeks... hard to know.)
Here's a cross section (in blue) and the second derivative (in tan), which changes sign at radius = 1.
answered Jan 23 at 0:30
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
$begingroup$
so it is impossible to find the area of circle?
$endgroup$
– Andy Lam
Jan 23 at 0:36
1
$begingroup$
Let me guess his circle is the boundary of the set of $(x,y)$ values for which the Hessian matrix is negative definite. And that his textbook or notebook has a non-standard definition of concavity.
$endgroup$
– kimchi lover
Jan 23 at 0:42
$begingroup$
that's right except I haven't learned about Hessian matrix so is there any way to find the that circle without using Hessian matrix?
$endgroup$
– Andy Lam
Jan 23 at 0:46
$begingroup$
@kimchilover: Given the level of sophistication of the OP (his reputation is $6$), I strongly doubt he's working with Hessians.
$endgroup$
– David G. Stork
Jan 23 at 0:46
$begingroup$
@AndyLam, maybe you should spell out exactly what "concavities of a function" means in your textbook or course? I think there is a terminology mismatch going on. To me, a function is concave on all of its range at once, or not; I'm afraid to you a function can be concave at particular points and not others. What is your official precise definition of "concave"?
$endgroup$
– kimchi lover
Jan 23 at 0:59
add a comment |
1
1
1
$begingroup$
The red circle shows where the curvature on the function changes sign. (Perhaps this is what the OP seeks... hard to know.)
Here's a cross section (in blue) and the second derivative (in tan), which changes sign at radius = 1.
answered Jan 23 at 0:30
David G. StorkDavid G. Stork
11.1k41432
$endgroup$
The red circle shows where the curvature on the function changes sign. (Perhaps this is what the OP seeks... hard to know.)
Here's a cross section (in blue) and the second derivative (in tan), which changes sign at radius = 1.
answered Jan 23 at 0:30
David G. StorkDavid G. Stork
11.1k41432
edited Jan 23 at 1:23
answered Jan 23 at 0:30
David G. StorkDavid G. Stork
11.1k41432
answered Jan 23 at 0:30
David G. StorkDavid G. Stork
11.1k41432
answered Jan 23 at 0:30
David G. StorkDavid G. Stork
11.1k41432
11.1k41432
$begingroup$
so it is impossible to find the area of circle?
$endgroup$
– Andy Lam
Jan 23 at 0:36
1
$begingroup$
Let me guess his circle is the boundary of the set of $(x,y)$ values for which the Hessian matrix is negative definite. And that his textbook or notebook has a non-standard definition of concavity.
$endgroup$
– kimchi lover
Jan 23 at 0:42
$begingroup$
that's right except I haven't learned about Hessian matrix so is there any way to find the that circle without using Hessian matrix?
$endgroup$
– Andy Lam
Jan 23 at 0:46
$begingroup$
@kimchilover: Given the level of sophistication of the OP (his reputation is $6$), I strongly doubt he's working with Hessians.
$endgroup$
– David G. Stork
Jan 23 at 0:46
$begingroup$
@AndyLam, maybe you should spell out exactly what "concavities of a function" means in your textbook or course? I think there is a terminology mismatch going on. To me, a function is concave on all of its range at once, or not; I'm afraid to you a function can be concave at particular points and not others. What is your official precise definition of "concave"?
$endgroup$
– kimchi lover
Jan 23 at 0:59
add a comment |
$begingroup$
so it is impossible to find the area of circle?
$endgroup$
– Andy Lam
Jan 23 at 0:36
1
$begingroup$
Let me guess his circle is the boundary of the set of $(x,y)$ values for which the Hessian matrix is negative definite. And that his textbook or notebook has a non-standard definition of concavity.
$endgroup$
– kimchi lover
Jan 23 at 0:42
$begingroup$
that's right except I haven't learned about Hessian matrix so is there any way to find the that circle without using Hessian matrix?
$endgroup$
– Andy Lam
Jan 23 at 0:46
$begingroup$
@kimchilover: Given the level of sophistication of the OP (his reputation is $6$), I strongly doubt he's working with Hessians.
$endgroup$
– David G. Stork
Jan 23 at 0:46
$begingroup$
@AndyLam, maybe you should spell out exactly what "concavities of a function" means in your textbook or course? I think there is a terminology mismatch going on. To me, a function is concave on all of its range at once, or not; I'm afraid to you a function can be concave at particular points and not others. What is your official precise definition of "concave"?
$endgroup$
– kimchi lover
Jan 23 at 0:59
$begingroup$
so it is impossible to find the area of circle?
$endgroup$
– Andy Lam
Jan 23 at 0:36
$begingroup$
so it is impossible to find the area of circle?
$endgroup$
– Andy Lam
Jan 23 at 0:36
1
1
$begingroup$
Let me guess his circle is the boundary of the set of $(x,y)$ values for which the Hessian matrix is negative definite. And that his textbook or notebook has a non-standard definition of concavity.
$endgroup$
– kimchi lover
Jan 23 at 0:42
$begingroup$
Let me guess his circle is the boundary of the set of $(x,y)$ values for which the Hessian matrix is negative definite. And that his textbook or notebook has a non-standard definition of concavity.
$endgroup$
– kimchi lover
Jan 23 at 0:42
$begingroup$
that's right except I haven't learned about Hessian matrix so is there any way to find the that circle without using Hessian matrix?
$endgroup$
– Andy Lam
Jan 23 at 0:46
$begingroup$
that's right except I haven't learned about Hessian matrix so is there any way to find the that circle without using Hessian matrix?
$endgroup$
– Andy Lam
Jan 23 at 0:46
$begingroup$
@kimchilover: Given the level of sophistication of the OP (his reputation is $6$), I strongly doubt he's working with Hessians.
$endgroup$
– David G. Stork
Jan 23 at 0:46
$begingroup$
@kimchilover: Given the level of sophistication of the OP (his reputation is $6$), I strongly doubt he's working with Hessians.
$endgroup$
– David G. Stork
Jan 23 at 0:46
$begingroup$
@AndyLam, maybe you should spell out exactly what "concavities of a function" means in your textbook or course? I think there is a terminology mismatch going on. To me, a function is concave on all of its range at once, or not; I'm afraid to you a function can be concave at particular points and not others. What is your official precise definition of "concave"?
$endgroup$
– kimchi lover
Jan 23 at 0:59
$begingroup$
@AndyLam, maybe you should spell out exactly what "concavities of a function" means in your textbook or course? I think there is a terminology mismatch going on. To me, a function is concave on all of its range at once, or not; I'm afraid to you a function can be concave at particular points and not others. What is your official precise definition of "concave"?
$endgroup$
– kimchi lover
Jan 23 at 0:59
add a comment |
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1
$begingroup$
Which circle? What radio is it?
$endgroup$
– El borito
Jan 23 at 0:24
$begingroup$
the circle is inside the graph of the function
$endgroup$
– Andy Lam
Jan 23 at 0:27