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)
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.