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 j^th 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

The Correct Option is A

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