# Are there polynomial functions whose graphs have: 11 points of inflection, but no max or min ?

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Are there polynomial functions whose graphs have:

1001 points of inflection, but no max or min ?

Are there polynomial functions whose graphs have:

1001 points of inflection, but no max or min ?

##### 1 Answer

See below.

#### Explanation:

You can build a polynomial with as many inflexion points as needed using the truncated series expansion for

For instance, an example for

The next plot shows

And finally the plot for

NOTE

Depending on