Convex function on closed interval?

[csc2iffy]

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

 

[Ray Vickson]

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