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## Homework Statement

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)

## Homework Equations

none

## 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.