How to determine local extrema for $f(x) = xcdot sin(x) ^ {sin(x)}$
up vote
2
down vote
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I need to find the local extrema points of the following function:
$f(x) = xcdotsin(x) ^ {sin(x)}$
I was already able to derive to this function:
$f'(x) = x (ln(sin(x))+1)cos(x)sin(x)^{sin(x)}+sin(x)^ {sin(x)}$
calculus derivatives trigonometry maxima-minima
edited Nov 23 at 20:02
David G. Stork
9,33721232
asked Nov 23 at 19:40
Phins
132
|
show 5 more comments
up vote
2
down vote
favorite
I need to find the local extrema points of the following function:
$f(x) = xcdotsin(x) ^ {sin(x)}$
I was already able to derive to this function:
$f'(x) = x (ln(sin(x))+1)cos(x)sin(x)^{sin(x)}+sin(x)^ {sin(x)}$
calculus derivatives trigonometry maxima-minima
edited Nov 23 at 20:02
David G. Stork
9,33721232
asked Nov 23 at 19:40
Phins
132
find $x$ where $f'(x)$ is equal to $0$. Then assess the sign change while crossing the roots
– Makina
Nov 23 at 19:45
This function is defined in $bigcuplimits_{ninmathbb Z}[2npi,2npi+pi]$.
– Federico
Nov 23 at 19:50
You first have to take into considerations the extreme points of the intervals
– Federico
Nov 23 at 19:51
Then your equation $f'=0$ inside these intervals is highly non-linear and trascendental...
– Federico
Nov 23 at 19:52
I don't think much can be said, except numerically
– Federico
Nov 23 at 19:53
|
show 5 more comments
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I need to find the local extrema points of the following function:
$f(x) = xcdotsin(x) ^ {sin(x)}$
I was already able to derive to this function:
$f'(x) = x (ln(sin(x))+1)cos(x)sin(x)^{sin(x)}+sin(x)^ {sin(x)}$
calculus derivatives trigonometry maxima-minima
edited Nov 23 at 20:02
David G. Stork
9,33721232
asked Nov 23 at 19:40
Phins
132
I need to find the local extrema points of the following function:
$f(x) = xcdotsin(x) ^ {sin(x)}$
I was already able to derive to this function:
$f'(x) = x (ln(sin(x))+1)cos(x)sin(x)^{sin(x)}+sin(x)^ {sin(x)}$
calculus derivatives trigonometry maxima-minima
calculus derivatives trigonometry maxima-minima
edited Nov 23 at 20:02
David G. Stork
9,33721232
asked Nov 23 at 19:40
Phins
132
edited Nov 23 at 20:02
David G. Stork
9,33721232
asked Nov 23 at 19:40
Phins
132
edited Nov 23 at 20:02
David G. Stork
9,33721232
edited Nov 23 at 20:02
David G. Stork
9,33721232
edited Nov 23 at 20:02
David G. Stork
9,33721232
9,33721232
asked Nov 23 at 19:40
Phins
132
asked Nov 23 at 19:40
Phins
132
asked Nov 23 at 19:40
Phins
132
132
find $x$ where $f'(x)$ is equal to $0$. Then assess the sign change while crossing the roots
– Makina
Nov 23 at 19:45
This function is defined in $bigcuplimits_{ninmathbb Z}[2npi,2npi+pi]$.
– Federico
Nov 23 at 19:50
You first have to take into considerations the extreme points of the intervals
– Federico
Nov 23 at 19:51
Then your equation $f'=0$ inside these intervals is highly non-linear and trascendental...
– Federico
Nov 23 at 19:52
I don't think much can be said, except numerically
– Federico
Nov 23 at 19:53
|
show 5 more comments
find $x$ where $f'(x)$ is equal to $0$. Then assess the sign change while crossing the roots
– Makina
Nov 23 at 19:45
This function is defined in $bigcuplimits_{ninmathbb Z}[2npi,2npi+pi]$.
– Federico
Nov 23 at 19:50
You first have to take into considerations the extreme points of the intervals
– Federico
Nov 23 at 19:51
Then your equation $f'=0$ inside these intervals is highly non-linear and trascendental...
– Federico
Nov 23 at 19:52
I don't think much can be said, except numerically
– Federico
Nov 23 at 19:53
find $x$ where $f'(x)$ is equal to $0$. Then assess the sign change while crossing the roots
– Makina
Nov 23 at 19:45
find $x$ where $f'(x)$ is equal to $0$. Then assess the sign change while crossing the roots
– Makina
Nov 23 at 19:45
This function is defined in $bigcuplimits_{ninmathbb Z}[2npi,2npi+pi]$.
– Federico
Nov 23 at 19:50
This function is defined in $bigcuplimits_{ninmathbb Z}[2npi,2npi+pi]$.
– Federico
Nov 23 at 19:50
You first have to take into considerations the extreme points of the intervals
– Federico
Nov 23 at 19:51
You first have to take into considerations the extreme points of the intervals
– Federico
Nov 23 at 19:51
Then your equation $f'=0$ inside these intervals is highly non-linear and trascendental...
– Federico
Nov 23 at 19:52
Then your equation $f'=0$ inside these intervals is highly non-linear and trascendental...
– Federico
Nov 23 at 19:52
I don't think much can be said, except numerically
– Federico
Nov 23 at 19:53
I don't think much can be said, except numerically
– Federico
Nov 23 at 19:53
|
show 5 more comments
1 Answer
1
active
oldest
votes
up vote
2
down vote
accepted
The domain of $f$ is where $sin x>0$ i.e. $$bigcup_{nin Bbb Z}(2npi ,2npi +pi)$$ on this domain by equaling the derivative to zero we obtain $$sin x^{sin x}=0\text{or}\ x(1+ln sin x)cos x+1=0$$where $sin x^{sin x}=0$ is always impossible and the second equation can only be solved numerically. Here is a sketch of the function
answered Nov 23 at 20:19
Mostafa Ayaz
13.6k3836
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
The domain of $f$ is where $sin x>0$ i.e. $$bigcup_{nin Bbb Z}(2npi ,2npi +pi)$$ on this domain by equaling the derivative to zero we obtain $$sin x^{sin x}=0\text{or}\ x(1+ln sin x)cos x+1=0$$where $sin x^{sin x}=0$ is always impossible and the second equation can only be solved numerically. Here is a sketch of the function
answered Nov 23 at 20:19
Mostafa Ayaz
13.6k3836
add a comment |
up vote
2
down vote
accepted
The domain of $f$ is where $sin x>0$ i.e. $$bigcup_{nin Bbb Z}(2npi ,2npi +pi)$$ on this domain by equaling the derivative to zero we obtain $$sin x^{sin x}=0\text{or}\ x(1+ln sin x)cos x+1=0$$where $sin x^{sin x}=0$ is always impossible and the second equation can only be solved numerically. Here is a sketch of the function
answered Nov 23 at 20:19
Mostafa Ayaz
13.6k3836
add a comment |
up vote
2
down vote
accepted
up vote
2
down vote
accepted
The domain of $f$ is where $sin x>0$ i.e. $$bigcup_{nin Bbb Z}(2npi ,2npi +pi)$$ on this domain by equaling the derivative to zero we obtain $$sin x^{sin x}=0\text{or}\ x(1+ln sin x)cos x+1=0$$where $sin x^{sin x}=0$ is always impossible and the second equation can only be solved numerically. Here is a sketch of the function
answered Nov 23 at 20:19
Mostafa Ayaz
13.6k3836
The domain of $f$ is where $sin x>0$ i.e. $$bigcup_{nin Bbb Z}(2npi ,2npi +pi)$$ on this domain by equaling the derivative to zero we obtain $$sin x^{sin x}=0\text{or}\ x(1+ln sin x)cos x+1=0$$where $sin x^{sin x}=0$ is always impossible and the second equation can only be solved numerically. Here is a sketch of the function
answered Nov 23 at 20:19
Mostafa Ayaz
13.6k3836
answered Nov 23 at 20:19
Mostafa Ayaz
13.6k3836
answered Nov 23 at 20:19
Mostafa Ayaz
13.6k3836
answered Nov 23 at 20:19
Mostafa Ayaz
13.6k3836
13.6k3836
add a comment |
add a comment |
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find $x$ where $f'(x)$ is equal to $0$. Then assess the sign change while crossing the roots
– Makina
Nov 23 at 19:45
This function is defined in $bigcuplimits_{ninmathbb Z}[2npi,2npi+pi]$.
– Federico
Nov 23 at 19:50
You first have to take into considerations the extreme points of the intervals
– Federico
Nov 23 at 19:51
Then your equation $f'=0$ inside these intervals is highly non-linear and trascendental...
– Federico
Nov 23 at 19:52
I don't think much can be said, except numerically
– Federico
Nov 23 at 19:53