What conjectures/predictions can you make about polynomial functions whose highest exponent is 6, or 7?

1 answer

degree 6: maximum of 6 real roots. Exactly 6 roots, if you include complex values.

shape is basically a steep parabola, with possible wiggles along the bottom somewhere. May open up or down.

It will have an absolute minimum/maximum somewhere.

Degree 7: at least one real root, total of 7 roots, including comples ones.

because of odd degree, will have a range of -oo to +oo.
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