if the graph of a polynomial has 3 local minimuns and 3 local maximums, then the equation must be at least to what power?

if the graph of a polynomial has 3 local minimuns and 3 local maximums, then the equation must be at least to what power?
if the graph of a polynomial has 3 local minimuns and 3 local maximums, then the equation must be at least to what power?

Is it the third power?? --don't quote me on that.
Do you know the equation? If you know that the degree is x to the largest power, the power being the degree.
Oh I hate math!!

1st power (a line) has 0 max and min
2nd power (parabola) has 1 max or min
3rd power has 2 max or min
4th power has 3 max or min

Let us suppose the polynomial is f(x)

There are 6 stationary points (Maximum/Minimum points)

Hence the equation : derivative of f(x) = 0 : must have at least 6 real roots

Hence derivative of f(x) must be of at least 6 degrees

Hence f(x) must be of at least 7 degrees

Hence, Power = at least 7