Understanding QuasiLinearity

newphysist

Hi,

I have two questions.

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

Code:

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

Vargo

What is the domain of your function?

newphysist

Real numbers R

haruspex

Quote by newphysist

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

Code:

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

This function is monotonic. And every monotonic function is quasilinear.

Similar Threads for: Understanding QuasiLinearity
Thread	Forum	Replies
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

Vargo	This function is monotonic. And every monotonic function is quasilinear.