Looks like you and I have the same maths class
Lake Tuggers ?
Either way, I'm looking for the exact same question. So looks like we won't have unique functions Crozius .
For the first, pick the first three values and arbitrarily decide the derivative at the third point should be -1.
For the second, start on the other end and match the derivative, since the problem statement says it has to be differentiable everywhere.
Really, just pick some functions out of a hat and make them do what you want. The derivative of -1 was 100% arbitrary.
The starting place is a function with arbitrary coefficients. Then you solve for the coefficients that make it do what you want.
