How to prove that there is a differentiable function $f$ such that $[f(x)]^{153}+f(x)+x=0$ for all $x$
1
$begingroup$
Prove that there is a differentiable function $f$ such that $[f(x)]^{153}+f(x)+x=0$ for all $x$. Furthermore, find $f'$ in terms of $f$.
To me I just write $y$ instead of all $f(x)$ and find that $x=-(y^{153}+y)$ If I just derive that would that be the solution of this question? If not what should i do to answer it appropriately.
calculus algebra-precalculus
edited Dec 8 '18 at 11:06
N. F. Taussig
44.2k93356
asked Dec 8 '18 at 10:57
HouseBTHouseBT
154
$endgroup$
add a comment |
1
$begingroup$
Prove that there is a differentiable function $f$ such that $[f(x)]^{153}+f(x)+x=0$ for all $x$. Furthermore, find $f'$ in terms of $f$.
To me I just write $y$ instead of all $f(x)$ and find that $x=-(y^{153}+y)$ If I just derive that would that be the solution of this question? If not what should i do to answer it appropriately.
calculus algebra-precalculus
edited Dec 8 '18 at 11:06
N. F. Taussig
44.2k93356
asked Dec 8 '18 at 10:57
HouseBTHouseBT
154
$endgroup$
$begingroup$
Please write titles that describe the problem you wish to solve rather than the course title. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:01
$begingroup$
Can you advise me a description for this problem? Because I am a bit confused about the description.
$endgroup$
– HouseBT
Dec 8 '18 at 11:04
$begingroup$
I just placed the question in the title (while avoiding the command form, which is interpreted as rude on this site).
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:07
$begingroup$
Oh okay now it is obvious to me. Thank you for helping.
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
add a comment |
1
1
1
$begingroup$
Prove that there is a differentiable function $f$ such that $[f(x)]^{153}+f(x)+x=0$ for all $x$. Furthermore, find $f'$ in terms of $f$.
To me I just write $y$ instead of all $f(x)$ and find that $x=-(y^{153}+y)$ If I just derive that would that be the solution of this question? If not what should i do to answer it appropriately.
calculus algebra-precalculus
edited Dec 8 '18 at 11:06
N. F. Taussig
44.2k93356
asked Dec 8 '18 at 10:57
HouseBTHouseBT
154
$endgroup$
Prove that there is a differentiable function $f$ such that $[f(x)]^{153}+f(x)+x=0$ for all $x$. Furthermore, find $f'$ in terms of $f$.
To me I just write $y$ instead of all $f(x)$ and find that $x=-(y^{153}+y)$ If I just derive that would that be the solution of this question? If not what should i do to answer it appropriately.
calculus algebra-precalculus
calculus algebra-precalculus
edited Dec 8 '18 at 11:06
N. F. Taussig
44.2k93356
asked Dec 8 '18 at 10:57
HouseBTHouseBT
154
edited Dec 8 '18 at 11:06
N. F. Taussig
44.2k93356
asked Dec 8 '18 at 10:57
HouseBTHouseBT
154
edited Dec 8 '18 at 11:06
N. F. Taussig
44.2k93356
edited Dec 8 '18 at 11:06
N. F. Taussig
44.2k93356
edited Dec 8 '18 at 11:06
N. F. Taussig
44.2k93356
44.2k93356
asked Dec 8 '18 at 10:57
HouseBTHouseBT
154
asked Dec 8 '18 at 10:57
HouseBTHouseBT
154
asked Dec 8 '18 at 10:57
HouseBTHouseBT
154
154
$begingroup$
Please write titles that describe the problem you wish to solve rather than the course title. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:01
$begingroup$
Can you advise me a description for this problem? Because I am a bit confused about the description.
$endgroup$
– HouseBT
Dec 8 '18 at 11:04
$begingroup$
I just placed the question in the title (while avoiding the command form, which is interpreted as rude on this site).
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:07
$begingroup$
Oh okay now it is obvious to me. Thank you for helping.
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
add a comment |
$begingroup$
Please write titles that describe the problem you wish to solve rather than the course title. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:01
$begingroup$
Can you advise me a description for this problem? Because I am a bit confused about the description.
$endgroup$
– HouseBT
Dec 8 '18 at 11:04
$begingroup$
I just placed the question in the title (while avoiding the command form, which is interpreted as rude on this site).
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:07
$begingroup$
Oh okay now it is obvious to me. Thank you for helping.
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
$begingroup$
Please write titles that describe the problem you wish to solve rather than the course title. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:01
$begingroup$
Please write titles that describe the problem you wish to solve rather than the course title. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:01
$begingroup$
Can you advise me a description for this problem? Because I am a bit confused about the description.
$endgroup$
– HouseBT
Dec 8 '18 at 11:04
$begingroup$
Can you advise me a description for this problem? Because I am a bit confused about the description.
$endgroup$
– HouseBT
Dec 8 '18 at 11:04
$begingroup$
I just placed the question in the title (while avoiding the command form, which is interpreted as rude on this site).
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:07
$begingroup$
I just placed the question in the title (while avoiding the command form, which is interpreted as rude on this site).
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:07
$begingroup$
Oh okay now it is obvious to me. Thank you for helping.
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
$begingroup$
Oh okay now it is obvious to me. Thank you for helping.
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
add a comment |
1 Answer
1
active
oldest
votes
0
$begingroup$
HINT:
If $x = -[f(x)]^{153} - f(x)$,
then $g(x) = -x^{153} - x$ is the inverse function of $f(x)$.
Then if you prove $g(x)$ is differentiable, what does it tell about its inverse function ?
answered Dec 8 '18 at 11:07
rsadhvikarsadhvika
1,7101228
$endgroup$
$begingroup$
Then it's inverse is differentiable?
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
$begingroup$
Yes, you may look at exercise 12.14 for a sample problem here
$endgroup$
– rsadhvika
Dec 8 '18 at 11:13
$begingroup$
@HouseBT Unless $g'$ vanishes.
$endgroup$
– Michael Hoppe
Dec 8 '18 at 11:14
$begingroup$
Thank you so much ^^
$endgroup$
– HouseBT
Dec 8 '18 at 11:15
$begingroup$
Np :) hope you do see why $g$ is the inverse of $f$.. (Initially I had a problem visualizing..)
$endgroup$
– rsadhvika
Dec 8 '18 at 11:17
|
show 1 more comment
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1 Answer
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oldest
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1 Answer
1
active
oldest
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active
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votes
0
$begingroup$
HINT:
If $x = -[f(x)]^{153} - f(x)$,
then $g(x) = -x^{153} - x$ is the inverse function of $f(x)$.
Then if you prove $g(x)$ is differentiable, what does it tell about its inverse function ?
answered Dec 8 '18 at 11:07
rsadhvikarsadhvika
1,7101228
$endgroup$
$begingroup$
Then it's inverse is differentiable?
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
$begingroup$
Yes, you may look at exercise 12.14 for a sample problem here
$endgroup$
– rsadhvika
Dec 8 '18 at 11:13
$begingroup$
@HouseBT Unless $g'$ vanishes.
$endgroup$
– Michael Hoppe
Dec 8 '18 at 11:14
$begingroup$
Thank you so much ^^
$endgroup$
– HouseBT
Dec 8 '18 at 11:15
$begingroup$
Np :) hope you do see why $g$ is the inverse of $f$.. (Initially I had a problem visualizing..)
$endgroup$
– rsadhvika
Dec 8 '18 at 11:17
|
show 1 more comment
0
$begingroup$
HINT:
If $x = -[f(x)]^{153} - f(x)$,
then $g(x) = -x^{153} - x$ is the inverse function of $f(x)$.
Then if you prove $g(x)$ is differentiable, what does it tell about its inverse function ?
answered Dec 8 '18 at 11:07
rsadhvikarsadhvika
1,7101228
$endgroup$
$begingroup$
Then it's inverse is differentiable?
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
$begingroup$
Yes, you may look at exercise 12.14 for a sample problem here
$endgroup$
– rsadhvika
Dec 8 '18 at 11:13
$begingroup$
@HouseBT Unless $g'$ vanishes.
$endgroup$
– Michael Hoppe
Dec 8 '18 at 11:14
$begingroup$
Thank you so much ^^
$endgroup$
– HouseBT
Dec 8 '18 at 11:15
$begingroup$
Np :) hope you do see why $g$ is the inverse of $f$.. (Initially I had a problem visualizing..)
$endgroup$
– rsadhvika
Dec 8 '18 at 11:17
|
show 1 more comment
0
0
0
$begingroup$
HINT:
If $x = -[f(x)]^{153} - f(x)$,
then $g(x) = -x^{153} - x$ is the inverse function of $f(x)$.
Then if you prove $g(x)$ is differentiable, what does it tell about its inverse function ?
answered Dec 8 '18 at 11:07
rsadhvikarsadhvika
1,7101228
$endgroup$
HINT:
If $x = -[f(x)]^{153} - f(x)$,
then $g(x) = -x^{153} - x$ is the inverse function of $f(x)$.
Then if you prove $g(x)$ is differentiable, what does it tell about its inverse function ?
answered Dec 8 '18 at 11:07
rsadhvikarsadhvika
1,7101228
answered Dec 8 '18 at 11:07
rsadhvikarsadhvika
1,7101228
answered Dec 8 '18 at 11:07
rsadhvikarsadhvika
1,7101228
answered Dec 8 '18 at 11:07
rsadhvikarsadhvika
1,7101228
1,7101228
$begingroup$
Then it's inverse is differentiable?
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
$begingroup$
Yes, you may look at exercise 12.14 for a sample problem here
$endgroup$
– rsadhvika
Dec 8 '18 at 11:13
$begingroup$
@HouseBT Unless $g'$ vanishes.
$endgroup$
– Michael Hoppe
Dec 8 '18 at 11:14
$begingroup$
Thank you so much ^^
$endgroup$
– HouseBT
Dec 8 '18 at 11:15
$begingroup$
Np :) hope you do see why $g$ is the inverse of $f$.. (Initially I had a problem visualizing..)
$endgroup$
– rsadhvika
Dec 8 '18 at 11:17
|
show 1 more comment
$begingroup$
Then it's inverse is differentiable?
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
$begingroup$
Yes, you may look at exercise 12.14 for a sample problem here
$endgroup$
– rsadhvika
Dec 8 '18 at 11:13
$begingroup$
@HouseBT Unless $g'$ vanishes.
$endgroup$
– Michael Hoppe
Dec 8 '18 at 11:14
$begingroup$
Thank you so much ^^
$endgroup$
– HouseBT
Dec 8 '18 at 11:15
$begingroup$
Np :) hope you do see why $g$ is the inverse of $f$.. (Initially I had a problem visualizing..)
$endgroup$
– rsadhvika
Dec 8 '18 at 11:17
$begingroup$
Then it's inverse is differentiable?
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
$begingroup$
Then it's inverse is differentiable?
$endgroup$
– HouseBT
Dec 8 '18 at 11:10
$begingroup$
Yes, you may look at exercise 12.14 for a sample problem here
$endgroup$
– rsadhvika
Dec 8 '18 at 11:13
$begingroup$
Yes, you may look at exercise 12.14 for a sample problem here
$endgroup$
– rsadhvika
Dec 8 '18 at 11:13
$begingroup$
@HouseBT Unless $g'$ vanishes.
$endgroup$
– Michael Hoppe
Dec 8 '18 at 11:14
$begingroup$
@HouseBT Unless $g'$ vanishes.
$endgroup$
– Michael Hoppe
Dec 8 '18 at 11:14
$begingroup$
Thank you so much ^^
$endgroup$
– HouseBT
Dec 8 '18 at 11:15
$begingroup$
Thank you so much ^^
$endgroup$
– HouseBT
Dec 8 '18 at 11:15
$begingroup$
Np :) hope you do see why $g$ is the inverse of $f$.. (Initially I had a problem visualizing..)
$endgroup$
– rsadhvika
Dec 8 '18 at 11:17
$begingroup$
Np :) hope you do see why $g$ is the inverse of $f$.. (Initially I had a problem visualizing..)
$endgroup$
– rsadhvika
Dec 8 '18 at 11:17
|
show 1 more comment
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$begingroup$
Please write titles that describe the problem you wish to solve rather than the course title. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:01
$begingroup$
Can you advise me a description for this problem? Because I am a bit confused about the description.
$endgroup$
– HouseBT
Dec 8 '18 at 11:04
$begingroup$
I just placed the question in the title (while avoiding the command form, which is interpreted as rude on this site).
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:07
$begingroup$
Oh okay now it is obvious to me. Thank you for helping.
$endgroup$
– HouseBT
Dec 8 '18 at 11:10