Mixing
Can point of inflection occur at a point where second derivative doesnot exist?
$begingroup$
I refered these questions
Definition of Point of Inflection
An inflection point where the second derivative doesn't exist?
What is inflection point?
I couldnt understand the necessary conditions for point of inflection.My specific doubt is
Can point of inflection occur at a point where the second derivative of a function is discontinuous?
In the image attached, the curves of the actual function, its second derivative and third derivative are given(from left to right correspondingly) Can the point x=b be an inflection point for the function.
calculus functions
asked Feb 1 at 7:04
MohanMohan
285
$endgroup$
add a comment |
$begingroup$
I refered these questions
Definition of Point of Inflection
An inflection point where the second derivative doesn't exist?
What is inflection point?
I couldnt understand the necessary conditions for point of inflection.My specific doubt is
Can point of inflection occur at a point where the second derivative of a function is discontinuous?
In the image attached, the curves of the actual function, its second derivative and third derivative are given(from left to right correspondingly) Can the point x=b be an inflection point for the function.
calculus functions
asked Feb 1 at 7:04
MohanMohan
285
$endgroup$
$begingroup$
You have answered your own question. math.stackexchange.com/questions/402459/… Yes a point where the second derivative is discontinuous at that point can be an inflection point.
$endgroup$
– Matthew Liu
Feb 1 at 7:34
$begingroup$
@Matthew Liu Ok.Thanks for answering.Does this mean the point x=b in the diagram can be a point of inflection for f(x) ?
$endgroup$
– Mohan
Feb 1 at 7:43
1
$begingroup$
I think it "point of inflection" is only defined as change in sign of the second derivative and that this change of sign does not need to be continuous and go through 0. But it was ages ago I even saw this expression.
$endgroup$
– mathreadler
Feb 1 at 8:06
$begingroup$
@mathreadler A point of inflection is a geometric property. It's a point where the tangent line crosses the graph.
$endgroup$
– B. Goddard
Feb 1 at 11:39
$begingroup$
@B.Goddard Hmm if you say so. I think last time I encountered the name was in high school... Definitely did not occur particularly often at university for me.
$endgroup$
– mathreadler
Feb 1 at 13:12
add a comment |
$begingroup$
I refered these questions
Definition of Point of Inflection
An inflection point where the second derivative doesn't exist?
What is inflection point?
I couldnt understand the necessary conditions for point of inflection.My specific doubt is
Can point of inflection occur at a point where the second derivative of a function is discontinuous?
In the image attached, the curves of the actual function, its second derivative and third derivative are given(from left to right correspondingly) Can the point x=b be an inflection point for the function.
calculus functions
asked Feb 1 at 7:04
MohanMohan
285
$endgroup$
I refered these questions
Definition of Point of Inflection
An inflection point where the second derivative doesn't exist?
What is inflection point?
I couldnt understand the necessary conditions for point of inflection.My specific doubt is
Can point of inflection occur at a point where the second derivative of a function is discontinuous?
In the image attached, the curves of the actual function, its second derivative and third derivative are given(from left to right correspondingly) Can the point x=b be an inflection point for the function.
calculus functions
calculus functions
asked Feb 1 at 7:04
MohanMohan
285
asked Feb 1 at 7:04
MohanMohan
285
edited Feb 1 at 7:25
Mohan
asked Feb 1 at 7:04
MohanMohan
285
asked Feb 1 at 7:04
MohanMohan
285
asked Feb 1 at 7:04
MohanMohan
285
285
$begingroup$
You have answered your own question. math.stackexchange.com/questions/402459/… Yes a point where the second derivative is discontinuous at that point can be an inflection point.
$endgroup$
– Matthew Liu
Feb 1 at 7:34
$begingroup$
@Matthew Liu Ok.Thanks for answering.Does this mean the point x=b in the diagram can be a point of inflection for f(x) ?
$endgroup$
– Mohan
Feb 1 at 7:43
1
$begingroup$
I think it "point of inflection" is only defined as change in sign of the second derivative and that this change of sign does not need to be continuous and go through 0. But it was ages ago I even saw this expression.
$endgroup$
– mathreadler
Feb 1 at 8:06
$begingroup$
@mathreadler A point of inflection is a geometric property. It's a point where the tangent line crosses the graph.
$endgroup$
– B. Goddard
Feb 1 at 11:39
$begingroup$
@B.Goddard Hmm if you say so. I think last time I encountered the name was in high school... Definitely did not occur particularly often at university for me.
$endgroup$
– mathreadler
Feb 1 at 13:12
add a comment |
$begingroup$
You have answered your own question. math.stackexchange.com/questions/402459/… Yes a point where the second derivative is discontinuous at that point can be an inflection point.
$endgroup$
– Matthew Liu
Feb 1 at 7:34
$begingroup$
@Matthew Liu Ok.Thanks for answering.Does this mean the point x=b in the diagram can be a point of inflection for f(x) ?
$endgroup$
– Mohan
Feb 1 at 7:43
1
$begingroup$
I think it "point of inflection" is only defined as change in sign of the second derivative and that this change of sign does not need to be continuous and go through 0. But it was ages ago I even saw this expression.
$endgroup$
– mathreadler
Feb 1 at 8:06
$begingroup$
@mathreadler A point of inflection is a geometric property. It's a point where the tangent line crosses the graph.
$endgroup$
– B. Goddard
Feb 1 at 11:39
$begingroup$
@B.Goddard Hmm if you say so. I think last time I encountered the name was in high school... Definitely did not occur particularly often at university for me.
$endgroup$
– mathreadler
Feb 1 at 13:12
$begingroup$
You have answered your own question. math.stackexchange.com/questions/402459/… Yes a point where the second derivative is discontinuous at that point can be an inflection point.
$endgroup$
– Matthew Liu
Feb 1 at 7:34
$begingroup$
You have answered your own question. math.stackexchange.com/questions/402459/… Yes a point where the second derivative is discontinuous at that point can be an inflection point.
$endgroup$
– Matthew Liu
Feb 1 at 7:34
$begingroup$
@Matthew Liu Ok.Thanks for answering.Does this mean the point x=b in the diagram can be a point of inflection for f(x) ?
$endgroup$
– Mohan
Feb 1 at 7:43
$begingroup$
@Matthew Liu Ok.Thanks for answering.Does this mean the point x=b in the diagram can be a point of inflection for f(x) ?
$endgroup$
– Mohan
Feb 1 at 7:43
1
1
$begingroup$
I think it "point of inflection" is only defined as change in sign of the second derivative and that this change of sign does not need to be continuous and go through 0. But it was ages ago I even saw this expression.
$endgroup$
– mathreadler
Feb 1 at 8:06
$begingroup$
I think it "point of inflection" is only defined as change in sign of the second derivative and that this change of sign does not need to be continuous and go through 0. But it was ages ago I even saw this expression.
$endgroup$
– mathreadler
Feb 1 at 8:06
$begingroup$
@mathreadler A point of inflection is a geometric property. It's a point where the tangent line crosses the graph.
$endgroup$
– B. Goddard
Feb 1 at 11:39
$begingroup$
@mathreadler A point of inflection is a geometric property. It's a point where the tangent line crosses the graph.
$endgroup$
– B. Goddard
Feb 1 at 11:39
$begingroup$
@B.Goddard Hmm if you say so. I think last time I encountered the name was in high school... Definitely did not occur particularly often at university for me.
$endgroup$
– mathreadler
Feb 1 at 13:12
$begingroup$
@B.Goddard Hmm if you say so. I think last time I encountered the name was in high school... Definitely did not occur particularly often at university for me.
$endgroup$
– mathreadler
Feb 1 at 13:12
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The short answer is "yes." An inflection point is a point where the tangent line crosses the graph of the function. So if the tangent line is vertical at a point, then the first derivative doesn't exist and therefore the second doesn't exist.
Take $y=sqrt[3]{x}$. Then $(0,0)$ is an inflection point, but the second derivative is discontinuous there.
answered Feb 1 at 11:43
B. GoddardB. Goddard
20.2k21543
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3095917%2fcan-point-of-inflection-occur-at-a-point-where-second-derivative-doesnot-exist%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The short answer is "yes." An inflection point is a point where the tangent line crosses the graph of the function. So if the tangent line is vertical at a point, then the first derivative doesn't exist and therefore the second doesn't exist.
Take $y=sqrt[3]{x}$. Then $(0,0)$ is an inflection point, but the second derivative is discontinuous there.
answered Feb 1 at 11:43
B. GoddardB. Goddard
20.2k21543
$endgroup$
add a comment |
$begingroup$
The short answer is "yes." An inflection point is a point where the tangent line crosses the graph of the function. So if the tangent line is vertical at a point, then the first derivative doesn't exist and therefore the second doesn't exist.
Take $y=sqrt[3]{x}$. Then $(0,0)$ is an inflection point, but the second derivative is discontinuous there.
answered Feb 1 at 11:43
B. GoddardB. Goddard
20.2k21543
$endgroup$
add a comment |
$begingroup$
The short answer is "yes." An inflection point is a point where the tangent line crosses the graph of the function. So if the tangent line is vertical at a point, then the first derivative doesn't exist and therefore the second doesn't exist.
Take $y=sqrt[3]{x}$. Then $(0,0)$ is an inflection point, but the second derivative is discontinuous there.
answered Feb 1 at 11:43
B. GoddardB. Goddard
20.2k21543
$endgroup$
The short answer is "yes." An inflection point is a point where the tangent line crosses the graph of the function. So if the tangent line is vertical at a point, then the first derivative doesn't exist and therefore the second doesn't exist.
Take $y=sqrt[3]{x}$. Then $(0,0)$ is an inflection point, but the second derivative is discontinuous there.
answered Feb 1 at 11:43
B. GoddardB. Goddard
20.2k21543
answered Feb 1 at 11:43
B. GoddardB. Goddard
20.2k21543
answered Feb 1 at 11:43
B. GoddardB. Goddard
20.2k21543
answered Feb 1 at 11:43
B. GoddardB. Goddard
20.2k21543
20.2k21543
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3095917%2fcan-point-of-inflection-occur-at-a-point-where-second-derivative-doesnot-exist%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
You have answered your own question. math.stackexchange.com/questions/402459/… Yes a point where the second derivative is discontinuous at that point can be an inflection point.
$endgroup$
– Matthew Liu
Feb 1 at 7:34
$begingroup$
@Matthew Liu Ok.Thanks for answering.Does this mean the point x=b in the diagram can be a point of inflection for f(x) ?
$endgroup$
– Mohan
Feb 1 at 7:43
1
$begingroup$
I think it "point of inflection" is only defined as change in sign of the second derivative and that this change of sign does not need to be continuous and go through 0. But it was ages ago I even saw this expression.
$endgroup$
– mathreadler
Feb 1 at 8:06
$begingroup$
@mathreadler A point of inflection is a geometric property. It's a point where the tangent line crosses the graph.
$endgroup$
– B. Goddard
Feb 1 at 11:39
$begingroup$
@B.Goddard Hmm if you say so. I think last time I encountered the name was in high school... Definitely did not occur particularly often at university for me.
$endgroup$
– mathreadler
Feb 1 at 13:12