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

If f(x)=sinx+2cos2x,π4x3π4. Then, f(x) attains its

A
minimum at x=π4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
maximum at x=π2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
minimum at π2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
maximum at x=sin1(14)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C minimum at π2
Given f(x)=sinx+2cos2x,x[π4,3π4]
f(x)=cosx4cosxsinx
and f′′(x)=sinx4cos2x
For maximum or minimum of f(x)
Put f(x)=0
cosx4cosx.sinx=0
cosx(14sinx)=0
cosx=0=cosπ2;sinx14
x[π4,3π4]x=π2
Now f′′(π2)=sinπ24cosπ
=1+4=3>0(min)
So, f(x) is minimum at x=π2
and its minimum value is
f(π2)=sinπ2+2cos2π2=12×0=1

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