Functions Question 392
Question: If $ f(x) $ is twice differentiable polynomial function such that $ f(1)=1,f(2)=-4,f(3)=9 $ , then
[IIT Screening 2005]
Options:
A) $ f’’(x)=2,\forall x\in R $
B) There exists at least one $ x\in (1,,3) $ such that $ f’’(x)=2 $
C) There exist at least one $ x\in (2,,3) $ such that $ f’(x)=5=f’’(x) $
D) There exist at least one $ x\in (1,,2) $ such that $ f(x)=3 $
Show Answer
Answer:
Correct Answer: B
Solution:
Let a function be $ g(x)=f(x)-x^{2} $
Þ $ g(x) $ has at least 3 real roots which are $ x=1 $ , 2 , 3
Þ $ g’(x) $ has at least 2 real roots in $ x\in (1,,3) $
Þ $ g’’(x) $ has at least 1 real roots in $ x\in (1,,3) $
Þ $ f’(x)=2 $ for at least one $ x\in (1,3) $ .
BETA
