1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# If f(x)=x2+2bx+2c2 and g(x)=−x2−2cx+b2, such that minimum f(x) > maximum g(x), then the relation b and c, is

A
no real value of b and c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
0<c<b2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
|c|>|b|2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
|c|<|b|2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C |c|>|b|√2Given : f(x)=x2+2bx+2c2 and g(x)=−x2−2cx+b2Differentiating f(x) and then equating with 0, we get 2x+2b=0x=−bso, now, f(−b) is the minimum f(x)now, differentiating g(x) and then equating with 0, we get −2x−2c=0x=−cso, now g(−c) is the maximum g(x)now, according to questionminimum f(x)>maximumg(x)f(−b)>g(−c)(−b)2+2b(−b)+2c2>−(−c)2−2c(−c)+b2b2−2b2+2c2>−c2+2c2+b2c2>2b2|c|>|b| √2

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
(x+y)^2
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program