About symmetric rank-1 random matrices

actual evaluation – Are such features differentiable? Answer

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actual evaluation – Are such features differentiable?

In my latest researches, I encountered features $f$ satisfying the next practical inequality:

$$
(*); f(x)geq f(y)(1+x-y) ; ; ; x,yin mathbb{R}.
$$

Since $f$ is convex (as a result of $displaystyle f(x)=sup_y [f(y)+f(y)(x-y)]$), it’s left and privilege differentiable. Also, it’s patent that each one features of the figure $f(t)=ce^t$ with $cgeq 0$ answer
$(*)$. Now, my questions:

(1) Is $f$ all over the place differentiable?

(2) Are there another options for $(*)$?

(3) Is this practical inequality well-known (any references
(paper, bespeak, web site, and so forth.) for such practical inequalities)?

Thanks in forward

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