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

If the function f(x)=(a23a+2)cosx2+(a1)x possesses critical points, then a belongs to the interval

A
(,0)(4,)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(,0][4,)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(,0]{1}[4,)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A (,0]{1}[4,)
Given
f(x)=(a23a+3)cosx2+(a1)x
f(x)=12(a1)(a2)sin(x2)+(a1)
f(x)=(a1)[112(a2)sin(x2)]
If f(x) possesses critical points, then
f(x)=0 (a1)[1(a22)sinx2]=0
a=1 and 1(a22)sinx2=0
a=1 and sin(x2)=2a2
a=1 and 2a21
a=1 and |a2|2
a=1 and a22 or a22
a=1 and a4 or a0
a=1 and a(,0][4,)
Therefore, a(,0]{1}[4,)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction to Limits
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon