Progression (Sequence and Series)Easy
Question
Let f(x) be a polynomial function of second degree. If f(1) = f(-1) and a, b, c are in A. P., then f′(a), f′(b) and f′(c) are in
Options
A.A.P.
B.G.P.
C.H. P.
D.arithmetic-geometric progression
Solution
f(x) = ax2 + bx + c
f(1) = a + b + c
f(-1) = a - b + c
⇒ a + b + c = a - b + c also 2b = a + c
f′(x) = 2ax + b = 2ax
f′(a) = 2a2
f′(b) = 2ab
f′(c) = 2ac
⇒ AP.
Hence, (A) is the correct answer.
f(1) = a + b + c
f(-1) = a - b + c
⇒ a + b + c = a - b + c also 2b = a + c
f′(x) = 2ax + b = 2ax
f′(a) = 2a2
f′(b) = 2ab
f′(c) = 2ac
⇒ AP.
Hence, (A) is the correct answer.
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