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
A convex function is a mathematical function where a line segment connecting any two points on the graph of the function never lies above the graph. This means that the function always curves towards or stays on or below the line connecting the two points.
The main difference between a convex function and a concave function is the direction of the curvature. A convex function curves upwards or stays flat, while a concave function curves downwards or stays flat.
Convex functions have many applications in mathematics, economics, and engineering. They are used to model optimization problems and to prove the existence of solutions to these problems. They also have important properties that make them easier to analyze and solve.
There are a few methods for determining if a function is convex. One way is to check the second derivative of the function. If the second derivative is always positive, then the function is convex. Another way is to check the graph of the function and see if it curves upwards or stays flat.
No, a function cannot be both convex and concave. This is because the direction of the curvature is opposite for convex and concave functions. However, a function can be neither convex nor concave, in which case it is called a non-convex function.