JEE Main & Advanced
Mathematics
Applications of Derivatives
Question Bank
Critical Thinking
question_answer
If \[f(x)={{x}^{2}}+2bx+2{{c}^{2}}\]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]
A)No real value of b and c
B)\[0<c<b\sqrt{2}\]
C)\[|c|<\,|b|\sqrt{2}\]
D)\[|c|\,>\,|b|\sqrt{2}\]
Correct Answer:
D
Solution :
\[f(x)={{(x+b)}^{2}}+2{{c}^{2}}-{{b}^{2}}\] is minimum at \[x=-b\] and \[g(x)={{b}^{2}}+{{c}^{2}}-{{(x+c)}^{2}}\] is maximum at \[x=-c\]