Differentiation Question 330
Question: Let $ f(x) $ be a polynomial function of the second degree. If $ f(1)=f(-1) $ and $ a_1,a_2,a_3 $ are in A.P. then $ {f}’(a_1) $ , $ {f}’(a_2) $ , $ {f}’(a_3) $ are in
[AMU 2005]
Options:
A) A.P
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ f(x)=ax^{2}+bx+c $
Then $ f’(x)=2ax+b $ also, $ f(1)=f(-1) $
$ a+b+c=a-b+c $
Therefore b = 0
$ \therefore $ $ {f}’(x)=2ax $ ;
$ \therefore $ $ {f}’(a_1)=2aa_1 $
$ {f}’(a{ _2})=2aa_2 $ , $ {f}’(a_3)=2aa_3 $
As $ a_1,a_2,a_3 $ are in A.P. $ {f}’(a_1),{f}’(a_2),{f}’(a_3) $ are in A.P.
BETA
