fourwindschill
New member
- Joined
- Feb 11, 2009
- Messages
- 5
Suppose that f: R->R is at least once differentiable. Prove, using direct proofs, that f is convex if and only if its first deriviative is non-decresing.
fourwindschill said: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.
fourwindschill said:Direct proofs, convexity, once differentiable.
We cannot assume that the function is twice differentiable, can we? Thats a greater restriction.....
Convexity is a type of concavity (the difference is the direction)... which is directly testable with the second derivative test. I dont see how, without second derivatives, we can possibly test concavity, directly.