Concave Function: Top Strategies to Solve

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

Neil Sharp 2022-11-25

Given a concave function $f (x)$ , why $f (x) - x f^{'} (x) > 0$ ?

Moncelliqo4 2022-11-25

Prove if $f$ is a concave function, then $f (\frac{a x_{1} + b x_{2} + c x_{3}}{a + b + c}) \geq \frac{a f (x_{1}) + b f (x_{2}) + c f (x_{3})}{a + b + c} .$

valahanyHcm 2022-11-24

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

Jazlyn Nash 2022-11-24

Suppose $γ \in R^{1}$ and $β \in R^{k}$ .
Let $f (γ, β) = (y_{2} - γ y_{1}) - (y_{3} - γ y_{2}) \exp (x^{'} β)$
Then is f a concave function of $(γ, β^{'})$ ?

Jamie Medina 2022-11-24

Given a function $f (x)$ on $R$ , and that $f (x)$ is strictly increasing and strictly concave: $f^{'} (x) > 0$ , and $f^{″} (x) < 0$ . Is it always true that, for such function, we have:
$f (a + b) < f (a) + f (b)$
$a, b$ 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:
$| | \nabla f (x) - \nabla f (y) | | \leq L | | x - y | |$
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 $f : Ω \subseteq R^{n} \to R_{\geq 0}$ be a continuous differentiable function over $Ω$ . Suppose that the function $f$ is concave, and fix two points $x = (x_{1}, \dots, x_{n}), y = (y_{1}, \dots, y_{n}) \in Ω$ , $x = (x_{1}, \dots, x_{n}), y = (y_{1}, \dots, y_{n}) \in Ω$ .
If $x_{i} \leq y_{i}$ for all $i = 1, \dots, n$ and $Ω = R^{n}$ , does it hold $∥ \nabla_{x} f ∥\geq∥ \nabla_{y} f ∥$ ?

inurbandojoa 2022-11-20

Let $f (x)$ be an increasing, strictly concave function with $f (0) = 0$ . Show that given $x < y$ , $f (y + ε) - f (x + ε) < f (y) - f (x)$ , where $ε$ is a small, positive number.

Adrian Brown 2022-11-20

Let $f \in C^{2}$ (i.e, $f$ is differentiable twice and $f^{'}, f^{″}$ are continuous. Show that $f$ can be written as $f (x) = g (x) + h (x)$ where $g (x)$ is convex for any $x$ and $h (x)$ 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
$c (p) = min_{x} \sum_{i = 1}^{n} x_{i} p_{i}$
subject to $f (x) \geq 1$ where $f : R_{+}^{n} \mapsto R$ is increasing and concave.

Humberto Campbell 2022-11-18

Let $f (x)$ be a non-negative and upper convex (concave) function defined on the interval $[a, b]$ . Suppose $f (\frac{a + b}{2}) \leq 2$ . Show that $f (x) \leq 4$ for all $x \in [a, b]$ .

Adison Rogers 2022-11-17

What would be a good function which is increasing, continuous, concave downward with
$lim_{x \to 0} f (x) = 0.5$
and
$lim_{x \to \infty} f (x) = 1.$
It should be concave downward whose concavity can be parametrically controlled.

Simone Watts 2022-11-17

Does there exist a concave function $f : (0, \infty) \to (0, \infty)$ with the following properties?
$f$ is $r$ -homogeneous for some $r > 0$ , i.e., $r > 0$ for all $x > 0$

Aron Heath 2022-11-16

How to show that the entropy $H (Pois (λ))$ of a Poisson distribution $Pois (λ)$ is Concave in parameter $λ$ ? i-e

Aliyah Thompson 2022-11-16

If $f : R \to R$ is a concave function such that $lim_{x \to \infty} (f (x) - f (x - 1)) = 0$ then $f$ increasing.

A concave function describes a curve bent inward, like the inside of a bowl. Examples include polynomials and logarithmic functions. To determine if a function is concave up or down, you can plot the equation on a graph or use derivatives. If the derivative is decreasing, the function is concave. If the derivative is increasing, it is convex. For more help with understanding concave functions, including equations and answers to specific problems, check out Plainmath many math tutors who are always available to help.

Calculus 1

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