# Recent questions in Concave Function

Recent questions in Concave Function
Marques Flynn 2022-11-25

### Mean value for a concave function over $\left[0,1\right]$ VS $f\left(1/2\right)$

Neil Sharp 2022-11-25

### Given a concave function $f\left(x\right)$, why $f\left(x\right)-x{f}^{\prime }\left(x\right)>0$?

Moncelliqo4 2022-11-25

### Prove if $f$ is a concave function, then $f\left(\frac{a{x}_{1}+b{x}_{2}+c{x}_{3}}{a+b+c}\right)\ge \frac{af\left({x}_{1}\right)+bf\left({x}_{2}\right)+cf\left({x}_{3}\right)}{a+b+c}.$

valahanyHcm 2022-11-24

### Is this function increasing/decreasing and convex/concave?$y=3x+\mathrm{ln}\left(\frac{3x-4}{x-1}\right)$

Jazlyn Nash 2022-11-24

### Suppose $\gamma \in {R}^{1}$ and $\beta \in {R}^{k}$.Let $f\left(\gamma ,\beta \right)=\left({y}_{2}-\gamma {y}_{1}\right)-\left({y}_{3}-\gamma {y}_{2}\right)\mathrm{exp}\left({x}^{\mathrm{\prime }}\beta \right)$Then is f a concave function of $\left(\gamma ,{\beta }^{\mathrm{\prime }}\right)$?

Jamie Medina 2022-11-24

### Given a function $f\left(x\right)$ on $R$, and that $f\left(x\right)$ is strictly increasing and strictly concave: ${f}^{\prime }\left(x\right)>0$, and ${f}^{″}\left(x\right)<0$. Is it always true that, for such function, we have:$f\left(a+b\right)$a,b$ are real numbers.

neimanjaLrq 2022-11-24

### Positive constant divided by a concave function, how to convexify this constraint?

Kyler Oconnor 2022-11-22

### Given a ${C}^{2}$ L-smooth function the Lipschitz condition is:$||\mathrm{\nabla }f\left(x\right)-\mathrm{\nabla }f\left(y\right)||\le L||x-y||$Are these conditions only true for convex ${C}^{2}$ function? What will change If $f$ is ${C}^{2}$ and concave?

Ty Moore 2022-11-22

### Does the property of non-increasing slope be generalized to a concave function for multiple variables?

unabuenanuevasld 2022-11-21

### Let $f:\mathrm{\Omega }\subseteq {\mathbb{R}}^{n}\to {\mathbb{R}}_{\ge 0}$ be a continuous differentiable function over $\mathrm{\Omega }$. Suppose that the function $f$ is concave, and fix two points $\mathbf{x}=\left({x}_{1},\dots ,{x}_{n}\right),\mathbf{y}=\left({y}_{1},\dots ,{y}_{n}\right)\in \mathrm{\Omega }$,$\mathbf{x}=\left({x}_{1},\dots ,{x}_{n}\right),\mathbf{y}=\left({y}_{1},\dots ,{y}_{n}\right)\in \mathrm{\Omega }$.If ${x}_{i}\le {y}_{i}$ for all $i=1,\dots ,n$ and $\mathrm{\Omega }={\mathbb{R}}^{n}$, does it hold $\parallel {\mathrm{\nabla }}_{\mathbf{x}}f\parallel \ge \parallel {\mathrm{\nabla }}_{\mathbf{y}}f\parallel$?

inurbandojoa 2022-11-20

### Let $f\in {\mathcal{C}}^{2}$ (i.e, $f$ is differentiable twice and ${f}^{\prime },{f}^{″}$ are continuous. Show that $f$ can be written as $f\left(x\right)=g\left(x\right)+h\left(x\right)$ where $g\left(x\right)$ is convex for any $x$ and $h\left(x\right)$ is concave for any $x$.

pin1ta4r3k7b 2022-11-19

### How to prove that the product of a decreasing monotonic function and a strictly increasing monotonic function is a concave function?

Jairo Hodges 2022-11-18

### Why must risk averse be correlated with a concave utility function?

spasiocuo43 2022-11-18

### Consider the optimization problem$c\left(p\right)=\underset{x}{min}\sum _{i=1}^{n}{x}_{i}{p}_{i}$subject to $f\left(x\right)\ge 1$ where $f:{\mathbb{R}}_{+}^{n}↦\mathbb{R}$ is increasing and concave.

Humberto Campbell 2022-11-18