The polynomial function f(x) = x^17-x has at most:
(A) 17 zeros and 17 turning points
(B) 17 zeros and 16 turning points
(C) 16 zeros and 16 turning points
(D) 16 zeros and 17 turning points
(E) no zeros and no turning points

Question

The polynomial function f(x) = x^17-x has at most: 
(A) 17 zeros and 17 turning points
(B) 17 zeros and 16 turning points
(C) 16 zeros and 16 turning points
(D) 16 zeros and 17 turning points
(E) no zeros and no turning points

anonymous · Answer

17 zeros because its a 17th power, and 16 turning points because if you look at a line, there are not turning points, a parabola, one, and by induction a 17th power should have 16