Can anyone help me prove the following inequality? Thanks!
1 Answer
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Hi Professor Mohamed,
$g(x)=T(\delta x)$
$k_{1}=f'^{-1}(g'(0))$
$f-g$ is increasing in the interval $[0,\hat{k}]$, $k_{1}$ belongs to this interval, so we have $(f-g)(\hat{k})>(f-g)(k_{1})$
remains to show that in $[0,k_{1}]$, the tangent in 0 of g is between the 2 curves : this tangent is above $ g$, because $g$ is concave, it is below $f$ because its coefficient is $f '(k_ {1})$ and it's $<f' (x) \forall x$ in $[0,k_{1}]$, because $f$ is concave