1. The problem statement, all variables and given/known data
Construct a piecewise function f(x) such that the following conditions are satisfied:
Concave down on (  infinity, 5)
Concave up on (5, infinity)
increasing over ( infinity,infinity)
Nonzero sloped tangent line at the point of inflection x = 5
f(5) = 11 (continuous at x = 5)
f ' (5) =6
3. The attempt at a solution
I really don't know what I should do to get started. My teacher assigned this as a homework problem without going over anything related to this. I could draw a graph to easily satisfy the given conditions, but I don't know how to find the equations of the curves I drew.If you could point me in the right direction I would really appreciate it.
