Question

Let p(x) = x57 + 3x10 - 21x3 + x2 + 21 and
$q(x)=p(x)+\sum\limits_{j=1}^{57}p^{(j)}(x) \ \text{for all }x \in \R,$
where p(j)(x) denotes the jth derivative of p(x). Then the function q admits

• A. NEITHER a global maximum NOR a global minimum on $\R$
• B. a global maximum but NOT a global minimum on $\R$
• C. a global minimum but NOT a global maximum on $\R$
• D. a global minimum and a global maximum on $\R$

Answer 1

Answer: (A)

NEITHER a global maximum NOR a global minimum on $\R$

Answer 2

The correct option is (A) : NEITHER a global maximum NOR a global minimum on $\R$.