If you have the following inequality:

$\sup_{[x_{k-1},x_k]}f(x'-x_{k-1})+\sup_{[x',x_{k}]}f(x_k-x')\geq \sup_{[x_{k-1},x_k]}f(x_k-x_{k-1})$

Let A B C denote the respective supremums in order. What does my professor mean by saying A≤C & B≤C implies
$A(x'-x_{k-1})+B(x_k-x')\leq C(x'-x_{k-1})+C(x_k-x')=C(x_k-x_{k-1})$

Question

If you have the following inequality:

$\sup_{[x_{k-1},x_k]}f(x'-x_{k-1})+\sup_{[x',x_{k}]}f(x_k-x')\geq \sup_{[x_{k-1},x_k]}f(x_k-x_{k-1})$

Let A B C denote the respective supremums in order. What does my professor mean by saying A≤C & B≤C implies 
$A(x'-x_{k-1})+B(x_k-x')\leq C(x'-x_{k-1})+C(x_k-x')=C(x_k-x_{k-1})$

swolesammy · Answer

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anonymous · Answer

God damn texing is a nightmare on this site.

anonymous · Answer

http://mathb.in/44622

anonymous · Answer

If you have the following inequality: 

$\sup_{[x_{k-1},x_k]}f(x'-x_{k-1})+\sup_{[x',x_{k}]}f(x_k-x')\geq \sup_{[x_{k-1},x_k]}f(x_k-x_{k-1})$ 

Let A B C denote the respective supremums in order. What does my professor mean by saying A≤C & B≤C implies 
$A(x'-x_{k-1})+B(x_k-x')\leq C(x'-x_{k-1})+C(x_k-x')=C(x_k-x_{k-1})$