Browse Questions

# If $f\;(x)$ is a two degree polynomial such that $f\;(3)=f\;(-3)$ and $a, b, c$ are in $AP$, then $f'(a)$, $f'(b)$ and $f'(c)$ are in

$(a)\;AP\qquad(b)\;GP\qquad(c)\;HP\qquad(d)\;None\;of\;these$

Explanation : $f\;(x)=Ax^2+Bx+C$
$f\;(3)=f(-3)$
$9A+3B+C=9A-3B+C$
$B=0$
$f\;(x)=Ax^2+C$
$f^{|}\;(x)=2Ax$
$f^{|}\;(a)=2Aa\quad\;f^{|}\;(b)=2Ab\quad\;f^{|}\;(c)=2Ac\quad$ So, if a,b,c are in AP.
$f^{|}\;(a)\;,f^{|}\;(b)\;and\;f^{|}\;(c)$ are also in AP.