Question

Let \( f(x) \) be a second degree polynomial. If \( f(1)=f(-1) \) and \( p,q,r \) are in A.P., then \( f'(p), f'(q), f'(r) \) are:

• A. in A.P.
• B. in G.P.
• C. in H.P.
• D. neither in A.P. nor G.P. nor H.P.

Hint:

If derivative is linear: \begin{itemize} \item Linear functions preserve arithmetic progression. \item A.P. inputs ⇒ A.P. outputs. \end{itemize}

Answer 1

The Correct Option is A