Convex function on closed interval?

csc2iffy
Messages
74
Reaction score
0

Homework Statement


Let K be the closed interval [0,1] and consider the function f(x)=x^2. Is f convex? Is f linear?

help please :/ i don't even know how to set this up to check, our teacher didn't even get to this in class yet!


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
csc2iffy said:

Homework Statement


Let K be the closed interval [0,1] and consider the function f(x)=x^2. Is f convex? Is f linear?

help please :/ i don't even know how to set this up to check, our teacher didn't even get to this in class yet!


Homework Equations





The Attempt at a Solution


What is the definition of a linear function? Does your f(x) satisfy that? What is the definition of a convex function? Does that apply to f(x)? If your teacher has not covered that material yet, is it nevertheless in your textbook? If not, you can use Google, or go to the library.

RGV
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

I Open interval or Closed interval in defining convex function
Replies
4
Views
3K
Proof involving convex function and concave function
Replies
6
Views
2K
How to Prove Inequality for Convex Sets in R^n?
Replies
8
Views
2K
Linearly independent functions with identically zero Wronskian
Replies
1
Views
1K
How to calculate primitive functions on maximal intervals for periodic functions?
Replies
4
Views
2K
I Question about convex property in Jensen's inequality
Replies
4
Views
2K
Determining Convexity: S2 and Operations that Preserve Convexity
Replies
2
Views
1K
Convexity & Strict Convexity of Functionals (function of a function)
Replies
4
Views
3K
Integration Regions: Convex and Continuous?
Replies
6
Views
1K
No. of solutions of an equation involving a defined function
Replies
6
Views
960

Hot Threads

Recent Insights

Back
Top