where .
Its graph has the same limiting direction at both ends, upward when and downward when . Since its derivative
is a cubic polynomial, a real quartic function
has at most three critical points. It has at most
four real zeros and can have 0, 1, 2, 3, or 4 distinct real
zeros.
.
Its graph has the same limiting direction at both ends, upward when 
and downward when 
. Since its derivative
is a cubic polynomial, a real quartic function
has at most three critical points. It has at most
four real zeros and can have 0, 1, 2, 3, or 4 distinct real
zeros.
