Applications Of Derivatives Question 230
Question: If $ f(x)=x^{2}+2bx+2c^{2} $ and $ g(x)=-x^{2}-2cx+b^{2} $ such that min $ f(x)> $ max $ g(x) $ , then the relation between b and c is
[IIT Screening 2003]
Options:
A) No real value of b and c
B) $ 0<c<b\sqrt{2} $
C) $ |c|<,|b|\sqrt{2} $
D) $ |c|,>,|b|\sqrt{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)={{(x+b)}^{2}}+2c^{2}-b^{2} $ is minimum at $ x=-b $ and $ g(x)=b^{2}+c^{2}-{{(x+c)}^{2}} $ is maximum at $ x=-c $
therefore $ 2c^{2}-b^{2}>b^{2}+c^{2}\Rightarrow |c|,>\sqrt{2}|b| $ .
BETA
