Question

If \( g(x) = p(x) = qx^n \), and \( p \) and \( q \) are constants, then at \( x = 0 \), \( g(x) \) will be:

• A. Maximum when \( p>0, q>0 \)
• B. Minimum when \( p>0, q<0 \)
• C. Minimum when \( p>0, q>0 \)
• D. Maximum when \( p>0, q<0 \)

Hint:

If degree \( n \) is even and coefficient is positive, the polynomial opens upwards — thus minimum at x = 0.

Answer 1

The Correct Option is C

Given: \[ g(x) = p(x) = qx^n \] Assume \( n \) is even (since question implies extremum), and \( p>0 \), \( q>0 \) Then \( g(x) = qx^n \) is a parabola upwards, so has minimum at \( x = 0 \) \[ g(0) = 0, \text{and } g(x)>0 \text{ for all } x \neq 0 \Rightarrow \boxed{\text{Minimum at } x = 0} \] Final Answer:
(c) Minimum when \( p>0, q>0 \)