Maximum and minimum values of $y=fracax^2+2bx+cAx^2+2Bx+C$What's the minimum value?Finding the maximum and minimum values of $f(x)=a^x+a^1/x$notation for minimum and maximum?Piecewise function and maximum/minMinimum of a maximum functionMaximum value of function given minimum valueMaximum and minimum for piecewise functionMaximum and minimum values of functionStrictly convex minimum and maximumFinding the minimum value of a function without using Calculus
Multi tool use
Animating wave motion in water
"Marked down as someone wanting to sell shares." What does that mean?
Turning a hard to access nut?
Recursively updating the MLE as new observations stream in
Print a physical multiplication table
Why is "la Gestapo" feminine?
Imaginary part of expression too difficult to calculate
Can "few" be used as a subject? If so, what is the rule?
Symbolism of 18 Journeyers
Pre-Employment Background Check With Consent For Future Checks
Was World War I a war of liberals against authoritarians?
How can an organ that provides biological immortality be unable to regenerate?
Air travel with refrigerated insulin
What is the difference between something being completely legal and being completely decriminalized?
What is the tangent at a sharp point on a curve?
How do researchers send unsolicited emails asking for feedback on their works?
Writing in a Christian voice
Is this Pascal's Matrix?
Exposing a company lying about themselves in a tightly knit industry: Is my career at risk on the long run?
Why do I have a large white artefact on the rendered image?
If I cast the Enlarge/Reduce spell on an arrow, what weapon could it count as?
PTIJ: Which Dr. Seuss books should one obtain?
label a part of commutative diagram
Single word to change groups
Maximum and minimum values of $y=fracax^2+2bx+cAx^2+2Bx+C$
What's the minimum value?Finding the maximum and minimum values of $f(x)=a^x+a^1/x$notation for minimum and maximum?Piecewise function and maximum/minMinimum of a maximum functionMaximum value of function given minimum valueMaximum and minimum for piecewise functionMaximum and minimum values of functionStrictly convex minimum and maximumFinding the minimum value of a function without using Calculus
$begingroup$
Prove that the maximum and minimum values of $y=fracax^2+2bx+cAx^2+2Bx+C$ are those for which $(ax^2+2bx+c)-y(Ax^2+2Bx+C)$ is a perfect square.
I tried to solve this problem using the value of $y'=0$.
Solving the I got $y=fracax+bAx+B$.
Now I need to prove that $T=(ax^2+2bx+c)-y(Ax^2+2Bx+C)$ is a perfect square by substituting the value of $y=fracax+bAx+B$ but failed.
functions
asked Mar 13 at 10:44
Samar Imam ZaidiSamar Imam Zaidi
1,5751520
$endgroup$
add a comment |
$begingroup$
Prove that the maximum and minimum values of $y=fracax^2+2bx+cAx^2+2Bx+C$ are those for which $(ax^2+2bx+c)-y(Ax^2+2Bx+C)$ is a perfect square.
I tried to solve this problem using the value of $y'=0$.
Solving the I got $y=fracax+bAx+B$.
Now I need to prove that $T=(ax^2+2bx+c)-y(Ax^2+2Bx+C)$ is a perfect square by substituting the value of $y=fracax+bAx+B$ but failed.
functions
asked Mar 13 at 10:44
Samar Imam ZaidiSamar Imam Zaidi
1,5751520
$endgroup$
$begingroup$
For a non-calculus approach, I suspect the method illustrated here can be used. Indeed, you can probably find this in the 1800s literature I allude to (I gave one specific reference).
$endgroup$
– Dave L. Renfro
Mar 13 at 11:08
add a comment |
$begingroup$
Prove that the maximum and minimum values of $y=fracax^2+2bx+cAx^2+2Bx+C$ are those for which $(ax^2+2bx+c)-y(Ax^2+2Bx+C)$ is a perfect square.
I tried to solve this problem using the value of $y'=0$.
Solving the I got $y=fracax+bAx+B$.
Now I need to prove that $T=(ax^2+2bx+c)-y(Ax^2+2Bx+C)$ is a perfect square by substituting the value of $y=fracax+bAx+B$ but failed.
functions
asked Mar 13 at 10:44
Samar Imam ZaidiSamar Imam Zaidi
1,5751520
$endgroup$
Prove that the maximum and minimum values of $y=fracax^2+2bx+cAx^2+2Bx+C$ are those for which $(ax^2+2bx+c)-y(Ax^2+2Bx+C)$ is a perfect square.
I tried to solve this problem using the value of $y'=0$.
Solving the I got $y=fracax+bAx+B$.
Now I need to prove that $T=(ax^2+2bx+c)-y(Ax^2+2Bx+C)$ is a perfect square by substituting the value of $y=fracax+bAx+B$ but failed.
functions
functions
asked Mar 13 at 10:44
Samar Imam ZaidiSamar Imam Zaidi
1,5751520
asked Mar 13 at 10:44
Samar Imam ZaidiSamar Imam Zaidi
1,5751520
asked Mar 13 at 10:44
Samar Imam ZaidiSamar Imam Zaidi
1,5751520
asked Mar 13 at 10:44
Samar Imam ZaidiSamar Imam Zaidi
1,5751520
asked Mar 13 at 10:44
Samar Imam ZaidiSamar Imam Zaidi
1,5751520
1,5751520
$begingroup$
For a non-calculus approach, I suspect the method illustrated here can be used. Indeed, you can probably find this in the 1800s literature I allude to (I gave one specific reference).
$endgroup$
– Dave L. Renfro
Mar 13 at 11:08
add a comment |
$begingroup$
For a non-calculus approach, I suspect the method illustrated here can be used. Indeed, you can probably find this in the 1800s literature I allude to (I gave one specific reference).
$endgroup$
– Dave L. Renfro
Mar 13 at 11:08
$begingroup$
For a non-calculus approach, I suspect the method illustrated here can be used. Indeed, you can probably find this in the 1800s literature I allude to (I gave one specific reference).
$endgroup$
– Dave L. Renfro
Mar 13 at 11:08
$begingroup$
For a non-calculus approach, I suspect the method illustrated here can be used. Indeed, you can probably find this in the 1800s literature I allude to (I gave one specific reference).
$endgroup$
– Dave L. Renfro
Mar 13 at 11:08
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint: By the quotient rule we get
$$y'=-2,frac Abx^2-Bax^2+Acx-Cax+Bc-Cb left( Ax^2+2,Bx+
C right) ^2
$$
answered Mar 13 at 11:45
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.9k42866
$endgroup$
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%2f3146402%2fmaximum-and-minimum-values-of-y-fracax22bxcax22bxc%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
$begingroup$
Hint: By the quotient rule we get
$$y'=-2,frac Abx^2-Bax^2+Acx-Cax+Bc-Cb left( Ax^2+2,Bx+
C right) ^2
$$
answered Mar 13 at 11:45
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.9k42866
$endgroup$
add a comment |
$begingroup$
Hint: By the quotient rule we get
$$y'=-2,frac Abx^2-Bax^2+Acx-Cax+Bc-Cb left( Ax^2+2,Bx+
C right) ^2
$$
answered Mar 13 at 11:45
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.9k42866
$endgroup$
add a comment |
$begingroup$
Hint: By the quotient rule we get
$$y'=-2,frac Abx^2-Bax^2+Acx-Cax+Bc-Cb left( Ax^2+2,Bx+
C right) ^2
$$
answered Mar 13 at 11:45
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.9k42866
$endgroup$
Hint: By the quotient rule we get
$$y'=-2,frac Abx^2-Bax^2+Acx-Cax+Bc-Cb left( Ax^2+2,Bx+
C right) ^2
$$
answered Mar 13 at 11:45
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.9k42866
answered Mar 13 at 11:45
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.9k42866
answered Mar 13 at 11:45
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.9k42866
answered Mar 13 at 11:45
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
77.9k42866
77.9k42866
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%2f3146402%2fmaximum-and-minimum-values-of-y-fracax22bxcax22bxc%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
Dy,7FO EkStxmXR ecP8Si9k ZC9UEQG,eDy4NLrMadWxcstDQKgbpgRflCWkwCQZjPFrFOGYhhQivo,r0zN5I,m,2Itagqdasr,WA
$begingroup$
For a non-calculus approach, I suspect the method illustrated here can be used. Indeed, you can probably find this in the 1800s literature I allude to (I gave one specific reference).
$endgroup$
– Dave L. Renfro
Mar 13 at 11:08