Suppose you have a graph of a polynomial function and you can see that the function increases without bound on both left and right ends, has 4 real zereos and has 5 turning points. Based on this information, what is the minimum degree of the polynomial?

Answer 1

So the 1st derivative has 5 solutions, indicating that the 1st derivative must have been a 5th degree, making the original function sixth degree function
It must have had some double roots, that is , touching the x-axis without crossing over gives us 2 equal roots.