Mixing
$xln(x)-x+1$ when $x=0$
$begingroup$
I have to determine global and local extrema of the above function which is defined in the interval $[0,e]$ and to determine the global ones I need to check the value in $0$ and in $e$ right?
In $e$ the value is 1, that's obvious, but what do I do with zero? I looked at a graph and apparently $f(0)=1$, but obviously $ln(0)$ is not defined since $f(x) to -infty$ as $x to 0$.
I'm a bit clueless as to what to do now so I would really appreciate it if someone explained what I should do
real-analysis functions logarithms
edited Jan 29 at 5:36
Mohammad Zuhair Khan
1,6792625
asked Jan 29 at 4:43
cassnxcassnx
11
$endgroup$
add a comment |
$begingroup$
I have to determine global and local extrema of the above function which is defined in the interval $[0,e]$ and to determine the global ones I need to check the value in $0$ and in $e$ right?
In $e$ the value is 1, that's obvious, but what do I do with zero? I looked at a graph and apparently $f(0)=1$, but obviously $ln(0)$ is not defined since $f(x) to -infty$ as $x to 0$.
I'm a bit clueless as to what to do now so I would really appreciate it if someone explained what I should do
real-analysis functions logarithms
edited Jan 29 at 5:36
Mohammad Zuhair Khan
1,6792625
asked Jan 29 at 4:43
cassnxcassnx
11
$endgroup$
add a comment |
$begingroup$
I have to determine global and local extrema of the above function which is defined in the interval $[0,e]$ and to determine the global ones I need to check the value in $0$ and in $e$ right?
In $e$ the value is 1, that's obvious, but what do I do with zero? I looked at a graph and apparently $f(0)=1$, but obviously $ln(0)$ is not defined since $f(x) to -infty$ as $x to 0$.
I'm a bit clueless as to what to do now so I would really appreciate it if someone explained what I should do
real-analysis functions logarithms
edited Jan 29 at 5:36
Mohammad Zuhair Khan
1,6792625
asked Jan 29 at 4:43
cassnxcassnx
11
$endgroup$
I have to determine global and local extrema of the above function which is defined in the interval $[0,e]$ and to determine the global ones I need to check the value in $0$ and in $e$ right?
In $e$ the value is 1, that's obvious, but what do I do with zero? I looked at a graph and apparently $f(0)=1$, but obviously $ln(0)$ is not defined since $f(x) to -infty$ as $x to 0$.
I'm a bit clueless as to what to do now so I would really appreciate it if someone explained what I should do
real-analysis functions logarithms
real-analysis functions logarithms
edited Jan 29 at 5:36
Mohammad Zuhair Khan
1,6792625
asked Jan 29 at 4:43
cassnxcassnx
11
edited Jan 29 at 5:36
Mohammad Zuhair Khan
1,6792625
asked Jan 29 at 4:43
cassnxcassnx
11
edited Jan 29 at 5:36
Mohammad Zuhair Khan
1,6792625
edited Jan 29 at 5:36
Mohammad Zuhair Khan
1,6792625
edited Jan 29 at 5:36
Mohammad Zuhair Khan
1,6792625
1,6792625
asked Jan 29 at 4:43
cassnxcassnx
11
asked Jan 29 at 4:43
cassnxcassnx
11
asked Jan 29 at 4:43
cassnxcassnx
11
11
add a comment |
add a comment |
1 Answer
1
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votes
$begingroup$
You seem to forget that $$lim_{xto 0^+} , x log(x)=0$$ For the remaining, consider the function
$$f(x)=x log (x)-x+1$$ Compute its first derivative, check where it does cancels and use the second derivative test to see if this corresponds to a maximum or a minimum.
answered Jan 29 at 4:50
Claude LeiboviciClaude Leibovici
125k1158135
$endgroup$
add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You seem to forget that $$lim_{xto 0^+} , x log(x)=0$$ For the remaining, consider the function
$$f(x)=x log (x)-x+1$$ Compute its first derivative, check where it does cancels and use the second derivative test to see if this corresponds to a maximum or a minimum.
answered Jan 29 at 4:50
Claude LeiboviciClaude Leibovici
125k1158135
$endgroup$
add a comment |
$begingroup$
You seem to forget that $$lim_{xto 0^+} , x log(x)=0$$ For the remaining, consider the function
$$f(x)=x log (x)-x+1$$ Compute its first derivative, check where it does cancels and use the second derivative test to see if this corresponds to a maximum or a minimum.
answered Jan 29 at 4:50
Claude LeiboviciClaude Leibovici
125k1158135
$endgroup$
add a comment |
$begingroup$
You seem to forget that $$lim_{xto 0^+} , x log(x)=0$$ For the remaining, consider the function
$$f(x)=x log (x)-x+1$$ Compute its first derivative, check where it does cancels and use the second derivative test to see if this corresponds to a maximum or a minimum.
answered Jan 29 at 4:50
Claude LeiboviciClaude Leibovici
125k1158135
$endgroup$
You seem to forget that $$lim_{xto 0^+} , x log(x)=0$$ For the remaining, consider the function
$$f(x)=x log (x)-x+1$$ Compute its first derivative, check where it does cancels and use the second derivative test to see if this corresponds to a maximum or a minimum.
answered Jan 29 at 4:50
Claude LeiboviciClaude Leibovici
125k1158135
answered Jan 29 at 4:50
Claude LeiboviciClaude Leibovici
125k1158135
answered Jan 29 at 4:50
Claude LeiboviciClaude Leibovici
125k1158135
answered Jan 29 at 4:50
Claude LeiboviciClaude Leibovici
125k1158135
125k1158135
add a comment |
add a comment |
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