1. The problem statement, all variables and given/known data Let f:[0,2]->R be defined as: if 0 =< x =< 1 then f(x) = 4(x^3) if 1 < x =< 2 then x = x^2 + 2 Prove or disprove: There exist c_1 , c_2 in R so that F:[0,2]-R defined as: if 0 =< x =< 1 then f(x) = x^4 + c_1 if 1 < x =< 2 then x = (x^3)/3 + 2x + c_2 2. Relevant equations 3. The attempt at a solution Now my question is, why don't any c_1,c_2 make F an AD of f? Can any shed some light on this? Thanks.