Upper bound for the sup of the first derivative
$begingroup$
Given $f : mathbb{R} to mathbb{R}$ which is twice differentiable and that
$M_0 = sup_{x in mathbb{R} } |f(x)|$
$M_1 = sup_{x in mathbb{R} } |f'(x)|$
$M_2 = sup_{x in mathbb{R} } |f''(x)|$
prove that $M_1^2 leq 2 M_0 M_2$ ?
I think a good approach is Taylor series but for what values !
real-analysis calculus
asked Jan 13 at 11:34
AhmadAhmad
2,5771725
$endgroup$
add a comment |
$begingroup$
Given $f : mathbb{R} to mathbb{R}$ which is twice differentiable and that
$M_0 = sup_{x in mathbb{R} } |f(x)|$
$M_1 = sup_{x in mathbb{R} } |f'(x)|$
$M_2 = sup_{x in mathbb{R} } |f''(x)|$
prove that $M_1^2 leq 2 M_0 M_2$ ?
I think a good approach is Taylor series but for what values !
real-analysis calculus
asked Jan 13 at 11:34
AhmadAhmad
2,5771725
$endgroup$
$begingroup$
math.stackexchange.com/questions/98320/…
$endgroup$
– Yanko
Jan 13 at 11:36
add a comment |
$begingroup$
Given $f : mathbb{R} to mathbb{R}$ which is twice differentiable and that
$M_0 = sup_{x in mathbb{R} } |f(x)|$
$M_1 = sup_{x in mathbb{R} } |f'(x)|$
$M_2 = sup_{x in mathbb{R} } |f''(x)|$
prove that $M_1^2 leq 2 M_0 M_2$ ?
I think a good approach is Taylor series but for what values !
real-analysis calculus
asked Jan 13 at 11:34
AhmadAhmad
2,5771725
$endgroup$
Given $f : mathbb{R} to mathbb{R}$ which is twice differentiable and that
$M_0 = sup_{x in mathbb{R} } |f(x)|$
$M_1 = sup_{x in mathbb{R} } |f'(x)|$
$M_2 = sup_{x in mathbb{R} } |f''(x)|$
prove that $M_1^2 leq 2 M_0 M_2$ ?
I think a good approach is Taylor series but for what values !
real-analysis calculus
real-analysis calculus
asked Jan 13 at 11:34
AhmadAhmad
2,5771725
asked Jan 13 at 11:34
AhmadAhmad
2,5771725
asked Jan 13 at 11:34
AhmadAhmad
2,5771725
asked Jan 13 at 11:34
AhmadAhmad
2,5771725
asked Jan 13 at 11:34
AhmadAhmad
2,5771725
2,5771725
$begingroup$
math.stackexchange.com/questions/98320/…
$endgroup$
– Yanko
Jan 13 at 11:36
add a comment |
$begingroup$
math.stackexchange.com/questions/98320/…
$endgroup$
– Yanko
Jan 13 at 11:36
$begingroup$
math.stackexchange.com/questions/98320/…
$endgroup$
– Yanko
Jan 13 at 11:36
$begingroup$
math.stackexchange.com/questions/98320/…
$endgroup$
– Yanko
Jan 13 at 11:36
add a comment |
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$begingroup$
math.stackexchange.com/questions/98320/…
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– Yanko
Jan 13 at 11:36