Newton Method: min & max
$begingroup$
I don't seem to find a way to prove this question; a,b two reals such as a R ; the function's class is C^2 , be
1- $f(a)<0<f(b)$
2- $f'>0 in [a,b]$
3- $f">0 in [a,b]$
a) prove the existence of m=min f'(x) and M=max f"(x) and prove that m and M are positive
real-analysis
asked Jan 7 at 21:00
Alae CherkaouiAlae Cherkaoui
104
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add a comment |
$begingroup$
I don't seem to find a way to prove this question; a,b two reals such as a R ; the function's class is C^2 , be
1- $f(a)<0<f(b)$
2- $f'>0 in [a,b]$
3- $f">0 in [a,b]$
a) prove the existence of m=min f'(x) and M=max f"(x) and prove that m and M are positive
real-analysis
asked Jan 7 at 21:00
Alae CherkaouiAlae Cherkaoui
104
$endgroup$
add a comment |
$begingroup$
I don't seem to find a way to prove this question; a,b two reals such as a R ; the function's class is C^2 , be
1- $f(a)<0<f(b)$
2- $f'>0 in [a,b]$
3- $f">0 in [a,b]$
a) prove the existence of m=min f'(x) and M=max f"(x) and prove that m and M are positive
real-analysis
asked Jan 7 at 21:00
Alae CherkaouiAlae Cherkaoui
104
$endgroup$
I don't seem to find a way to prove this question; a,b two reals such as a R ; the function's class is C^2 , be
1- $f(a)<0<f(b)$
2- $f'>0 in [a,b]$
3- $f">0 in [a,b]$
a) prove the existence of m=min f'(x) and M=max f"(x) and prove that m and M are positive
real-analysis
real-analysis
asked Jan 7 at 21:00
Alae CherkaouiAlae Cherkaoui
104
asked Jan 7 at 21:00
Alae CherkaouiAlae Cherkaoui
104
asked Jan 7 at 21:00
Alae CherkaouiAlae Cherkaoui
104
asked Jan 7 at 21:00
Alae CherkaouiAlae Cherkaoui
104
asked Jan 7 at 21:00
Alae CherkaouiAlae Cherkaoui
104
104
add a comment |
add a comment |
1 Answer
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$begingroup$
Your question seems to be strange. $f'$ and $f''$ are continuous functions on the compact interval $[a,b]$, so they have a minimum and a maximum and since $f',f'' >0$, both of them have to be positive. For this, the first equation is not needed.
answered Jan 7 at 21:19
SchlubbidubbiSchlubbidubbi
914
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add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
Your question seems to be strange. $f'$ and $f''$ are continuous functions on the compact interval $[a,b]$, so they have a minimum and a maximum and since $f',f'' >0$, both of them have to be positive. For this, the first equation is not needed.
answered Jan 7 at 21:19
SchlubbidubbiSchlubbidubbi
914
$endgroup$
add a comment |
$begingroup$
Your question seems to be strange. $f'$ and $f''$ are continuous functions on the compact interval $[a,b]$, so they have a minimum and a maximum and since $f',f'' >0$, both of them have to be positive. For this, the first equation is not needed.
answered Jan 7 at 21:19
SchlubbidubbiSchlubbidubbi
914
$endgroup$
add a comment |
$begingroup$
Your question seems to be strange. $f'$ and $f''$ are continuous functions on the compact interval $[a,b]$, so they have a minimum and a maximum and since $f',f'' >0$, both of them have to be positive. For this, the first equation is not needed.
answered Jan 7 at 21:19
SchlubbidubbiSchlubbidubbi
914
$endgroup$
Your question seems to be strange. $f'$ and $f''$ are continuous functions on the compact interval $[a,b]$, so they have a minimum and a maximum and since $f',f'' >0$, both of them have to be positive. For this, the first equation is not needed.
answered Jan 7 at 21:19
SchlubbidubbiSchlubbidubbi
914
answered Jan 7 at 21:19
SchlubbidubbiSchlubbidubbi
914
answered Jan 7 at 21:19
SchlubbidubbiSchlubbidubbi
914
answered Jan 7 at 21:19
SchlubbidubbiSchlubbidubbi
914
914
add a comment |
add a comment |
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