Let p(x) = x57 + 3x10 − 21x3 + x2 + 21 and
q(x) = p(x) + \(\displaystyle\sum^{57}_{j=1}\) p(j) (x) for all x ∈ ℝ,
where p(j) (x) denotes the jth derivative of p(x). Then the function q admits
1
NEITHER a global maximum NOR a global minimum on ℝ
2
a global maximum but NOT a global minimum on ℝ
3
a global minimum but NOT a global maximum on ℝ
4
a global minimum and a global maximum on ℝ