True or false The graph of a polynomial function of degree n has at most n-1 turning point?

1 Answer
turksvids
Jan 13, 2018

True.

Explanation:

I'm not aware of a non-calculus based proof of this.

From a calculus perspective an nth degree polynomial has a derivative that is an n-1 degree polynomial. The derivative can have at most n-1 zeros and the zeros of the derivative are the potential turning points of the original polynomial. So you can have at most n-1 turning points.

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