Let
be a polynomial function of degree d ≥ 1 {\displaystyle {}d\geq 1} . Let m {\displaystyle {}m} be the number of local maxima of f {\displaystyle {}f} and n {\displaystyle {}n} the number of local minima of f {\displaystyle {}f} . Prove that if d {\displaystyle {}d} is odd then m = n {\displaystyle {}m=n} and that if d {\displaystyle {}d} is even then