thelazyman
Junior Member
- Joined
- Jan 14, 2006
- Messages
- 58
Hi, I have a problem with the following question:
Suppose that f: R----> R is at least once differentiable. Prove using direct proofs, that f is convex if and only if its first derivative is non-decreasing.
I get the function when using direct proofs, im assuming it is a continuous derivative
So i try to solve it using the limit function.
Lim x1--> x0 = f (x1) - f (x0)/ x1- x0 = f'(x0)
From there I do not where to go and i am trying to understand the question, i need this for an assignment, if someone can help me out with how to get the answer it would be greatly appreciated.
Thanks
Suppose that f: R----> R is at least once differentiable. Prove using direct proofs, that f is convex if and only if its first derivative is non-decreasing.
I get the function when using direct proofs, im assuming it is a continuous derivative
So i try to solve it using the limit function.
Lim x1--> x0 = f (x1) - f (x0)/ x1- x0 = f'(x0)
From there I do not where to go and i am trying to understand the question, i need this for an assignment, if someone can help me out with how to get the answer it would be greatly appreciated.
Thanks