wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The value of n, for which the function f(x)=(x24)n(x2x+1),nN assumes a local minima at x=2, is

A
an even number
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
an odd number
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
an irrational number
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
cannot be determined
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A an even number
We have f(x)=(x24)n(x2x+1) assumes local minima at x=2
f(2)<f(2h) and f(2)<f(2+h), where h>0
Since f(2)=0f(2h)>0 and f(2+h)>0,h>0
(h)n(4h)n[h23h+1]>0 and (h)n(4+h)n[h2+5h+1]>0
(h)n>0[(4h)>0,h23h+1>0,4+h>0,h2+5h+1>0h>0]
n is an even number

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Some Functions and Their Graphs
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon