Understanding QuasiLinearity


by newphysist
Tags: quasi linear
newphysist
newphysist is offline
#1
Nov13-12, 06:39 PM
P: 12
Hi,

I have two questions.

(1) I am trying to understand how the following function is quasi-linear:

f = min(1/2,x,x^2)
For it to be quasi linear it has to be quasi convex and quasi concave at same time.

(2) I think the reason the above function is not concave is cause on a certain interval (0,1) f = x^2 which is convex. Am I correct in my reasoning?

Thanks guys
Phys.Org News Partner Mathematics news on Phys.org
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Pseudo-mathematics and financial charlatanism
Vargo
Vargo is offline
#2
Nov13-12, 06:56 PM
P: 350
What is the domain of your function?
newphysist
newphysist is offline
#3
Nov13-12, 06:58 PM
P: 12
Real numbers R

haruspex
haruspex is offline
#4
Nov13-12, 07:22 PM
Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,179

Understanding QuasiLinearity


Quote Quote by newphysist View Post
(1) I am trying to understand how the following function is quasi-linear:
f = min(1/2,x,x^2)
For it to be quasi linear it has to be quasi convex and quasi concave at same time.
Yes. Which it is.
(2) I think the reason the above function is not concave is cause on a certain interval (0,1) f = x^2 which is convex. Am I correct in my reasoning?
Yes, though it would be more accurate to observe that on (0, 1/√2) it is not concave. (min{.5, x/2, x} would have been concave.)
Vargo
Vargo is offline
#5
Nov14-12, 08:59 AM
P: 350
This function is monotonic. And every monotonic function is quasilinear.


Register to reply

Related Discussions
gas law understanding General Physics 0
Is understanding one branch of math conducive to understanding another? General Math 4
understanding the big bad General Astronomy 26
I need a better understanding Introductory Physics Homework 3
Understanding this saying General Discussion 5