I know that the derivative of an even degree polynomial is odd, hence the derivative must have at least one real solution. But, this real solution could correspond to an inflection point as well. So, how do I prove in general that an even degree polynomial must have at least one turning point ?
Edit : I don't know if a constant function counts as an even degree polynomial, but regardless let us exclude that case.
Edit 2: A turning point is a point where the derivative changes sign. A turning point must also be a local maximum or local minimum.