Let be a twice differentiable function such that
If , find an explicit formula of .
We have successively
Let be a convex function on a convex domain and a convex non-decreasing function on . Prove that the composition of is convex on .
We want to prove that for it holds that
Let denote the golden ratio. Solve the equation
First of all we note that
We easily note that is one root of the equation, hence using Horner we get that
Hence is a double root and the other root is .
Let be similar to . Does hold?
No! Take then . The matrices are similar but not equal.