Prove the Form of a Function
$begingroup$
I asked a related question in oder to tackle this problem by myself, but still couldn't find a way to solve it despite a lot of efforts.
A function $f : R^2 to R$ satisfies $f(tx,ty) = t^2f(x, y)$ for all $t,x,y in R$. Assuming that
$f$ is continuously twice differentiable, show that:
$$
f(x,y) = ax^2 + bxy + cy^2
$$ for some
constants $a,b,c in R$.
calculus polynomials
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
463213
$endgroup$
add a comment |
$begingroup$
I asked a related question in oder to tackle this problem by myself, but still couldn't find a way to solve it despite a lot of efforts.
A function $f : R^2 to R$ satisfies $f(tx,ty) = t^2f(x, y)$ for all $t,x,y in R$. Assuming that
$f$ is continuously twice differentiable, show that:
$$
f(x,y) = ax^2 + bxy + cy^2
$$ for some
constants $a,b,c in R$.
calculus polynomials
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
463213
$endgroup$
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36
add a comment |
$begingroup$
I asked a related question in oder to tackle this problem by myself, but still couldn't find a way to solve it despite a lot of efforts.
A function $f : R^2 to R$ satisfies $f(tx,ty) = t^2f(x, y)$ for all $t,x,y in R$. Assuming that
$f$ is continuously twice differentiable, show that:
$$
f(x,y) = ax^2 + bxy + cy^2
$$ for some
constants $a,b,c in R$.
calculus polynomials
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
463213
$endgroup$
I asked a related question in oder to tackle this problem by myself, but still couldn't find a way to solve it despite a lot of efforts.
A function $f : R^2 to R$ satisfies $f(tx,ty) = t^2f(x, y)$ for all $t,x,y in R$. Assuming that
$f$ is continuously twice differentiable, show that:
$$
f(x,y) = ax^2 + bxy + cy^2
$$ for some
constants $a,b,c in R$.
calculus polynomials
calculus polynomials
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
463213
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
463213
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
463213
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
463213
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
463213
463213
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36
add a comment |
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36
add a comment |
0
active
oldest
votes
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%2f3074666%2fprove-the-form-of-a-function%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3074666%2fprove-the-form-of-a-function%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
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36