1. The problem statement, all variables and given/known data The following five points lie on a function: (1, 20), (2, 4), (5, 3), (6, 2), and (10, 1). Find an equation which passes through these points, and which also has the following: . . .i) three inflection points . . .ii) at least one local maximum . . .iii) at least one local minimum . . .iv) at least one critical point which differs from the listed points (above) . . .v) the property that it is continuous and differentiable throughout . . .vi) a piecewise definition (that is, it is not a single polynomial) 2. Relevant equations none 3. The attempt at a solution Actually, can you guys help me understand the question better. Also, the fact that the graph has to be piece-wise makes it harder. Can anyone offer me a reasonable solution? I need this urgently since it's due tomorrow. Any help would be great. Thanks.