Method to determine type of stationary point without calculating second derivative? The 2019 Stack Overflow Developer Survey Results Are InDerivative for logWhat exactly is a stationary point?Strictly monotone real function: stationary point, non-differentiable pointDeriving stationary points using the second order derivative.Why does the second derivative method allow us to classify stationary points?This second derivative is showing a point of inflection rather than a minimum pointHow can i find a stationary point despite a contradiction in its first derivative?Why doesn't conical surface have a stationary (critical) point (at 0,0)?Finding the stationary point of a type of hyperbola?Can a second derivative exist if the first derivative is undefined?
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Method to determine type of stationary point without calculating second derivative?
The 2019 Stack Overflow Developer Survey Results Are InDerivative for logWhat exactly is a stationary point?Strictly monotone real function: stationary point, non-differentiable pointDeriving stationary points using the second order derivative.Why does the second derivative method allow us to classify stationary points?This second derivative is showing a point of inflection rather than a minimum pointHow can i find a stationary point despite a contradiction in its first derivative?Why doesn't conical surface have a stationary (critical) point (at 0,0)?Finding the stationary point of a type of hyperbola?Can a second derivative exist if the first derivative is undefined?
$begingroup$
I have the function $$y= fracc+dx^22(bx-a)$$ where a,b,c,d are real constants and $c,d > 0$ . I have calculated it’s stationary points to be $$x=fraca pm sqrta^2+b^2 fraccdb$$ . I want to determine which one is the maximum/minimum without calculating the second derivative or plotting a graph when fixing the constants a,b,c,d. Is there any way I can do this?
calculus derivatives stationary-point
edited Apr 7 at 21:33
Maria Mazur
49.9k1361125
asked Apr 7 at 21:10
mailrenegademailrenegade
244
$endgroup$
add a comment |
$begingroup$
I have the function $$y= fracc+dx^22(bx-a)$$ where a,b,c,d are real constants and $c,d > 0$ . I have calculated it’s stationary points to be $$x=fraca pm sqrta^2+b^2 fraccdb$$ . I want to determine which one is the maximum/minimum without calculating the second derivative or plotting a graph when fixing the constants a,b,c,d. Is there any way I can do this?
calculus derivatives stationary-point
edited Apr 7 at 21:33
Maria Mazur
49.9k1361125
asked Apr 7 at 21:10
mailrenegademailrenegade
244
$endgroup$
add a comment |
$begingroup$
I have the function $$y= fracc+dx^22(bx-a)$$ where a,b,c,d are real constants and $c,d > 0$ . I have calculated it’s stationary points to be $$x=fraca pm sqrta^2+b^2 fraccdb$$ . I want to determine which one is the maximum/minimum without calculating the second derivative or plotting a graph when fixing the constants a,b,c,d. Is there any way I can do this?
calculus derivatives stationary-point
edited Apr 7 at 21:33
Maria Mazur
49.9k1361125
asked Apr 7 at 21:10
mailrenegademailrenegade
244
$endgroup$
I have the function $$y= fracc+dx^22(bx-a)$$ where a,b,c,d are real constants and $c,d > 0$ . I have calculated it’s stationary points to be $$x=fraca pm sqrta^2+b^2 fraccdb$$ . I want to determine which one is the maximum/minimum without calculating the second derivative or plotting a graph when fixing the constants a,b,c,d. Is there any way I can do this?
calculus derivatives stationary-point
calculus derivatives stationary-point
edited Apr 7 at 21:33
Maria Mazur
49.9k1361125
asked Apr 7 at 21:10
mailrenegademailrenegade
244
edited Apr 7 at 21:33
Maria Mazur
49.9k1361125
asked Apr 7 at 21:10
mailrenegademailrenegade
244
edited Apr 7 at 21:33
Maria Mazur
49.9k1361125
edited Apr 7 at 21:33
Maria Mazur
49.9k1361125
edited Apr 7 at 21:33
Maria Mazur
49.9k1361125
49.9k1361125
asked Apr 7 at 21:10
mailrenegademailrenegade
244
asked Apr 7 at 21:10
mailrenegademailrenegade
244
asked Apr 7 at 21:10
mailrenegademailrenegade
244
244
add a comment |
add a comment |
1 Answer
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$begingroup$
Yes, you can. If $b>0$ then for $xto infty $ the $y$ increases, thus at $x=a+...over b$ you have local minimum and at the second stationary point you have local maximum.
If $b<0$ you have to reverse all I said before. And if $b=0$ you have a quadratic equation function...
answered Apr 7 at 21:36
Maria MazurMaria Mazur
49.9k1361125
$endgroup$
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Yes, you can. If $b>0$ then for $xto infty $ the $y$ increases, thus at $x=a+...over b$ you have local minimum and at the second stationary point you have local maximum.
If $b<0$ you have to reverse all I said before. And if $b=0$ you have a quadratic equation function...
answered Apr 7 at 21:36
Maria MazurMaria Mazur
49.9k1361125
$endgroup$
add a comment |
$begingroup$
Yes, you can. If $b>0$ then for $xto infty $ the $y$ increases, thus at $x=a+...over b$ you have local minimum and at the second stationary point you have local maximum.
If $b<0$ you have to reverse all I said before. And if $b=0$ you have a quadratic equation function...
answered Apr 7 at 21:36
Maria MazurMaria Mazur
49.9k1361125
$endgroup$
add a comment |
$begingroup$
Yes, you can. If $b>0$ then for $xto infty $ the $y$ increases, thus at $x=a+...over b$ you have local minimum and at the second stationary point you have local maximum.
If $b<0$ you have to reverse all I said before. And if $b=0$ you have a quadratic equation function...
answered Apr 7 at 21:36
Maria MazurMaria Mazur
49.9k1361125
$endgroup$
Yes, you can. If $b>0$ then for $xto infty $ the $y$ increases, thus at $x=a+...over b$ you have local minimum and at the second stationary point you have local maximum.
If $b<0$ you have to reverse all I said before. And if $b=0$ you have a quadratic equation function...
answered Apr 7 at 21:36
Maria MazurMaria Mazur
49.9k1361125
edited Apr 7 at 21:43
answered Apr 7 at 21:36
Maria MazurMaria Mazur
49.9k1361125
answered Apr 7 at 21:36
Maria MazurMaria Mazur
49.9k1361125
answered Apr 7 at 21:36
Maria MazurMaria Mazur
49.9k1361125
49.9k1361125
add a comment |
add a comment |
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