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

Let f(x)={x,x1x2+ax+b,x>1,
If f(x) is differentiable at x=1, then

A
a=1, b=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
a=1, b=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a=1, b=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a=1, b=1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D a=1, b=1
f(x)={x,x1x2+ax+b,x>1
f(x)={1,x<12x+a,x>1

f(x) is differentiable at x=1
Then, it must be continuous at x=1
lim x1+f(x)=lim x1f(x)
1+a+b=1
a+b=0

Also, f(1+)=f(1)
lim x1+f(x)=lim x1f(x)
2+a=1
a=1
b=1

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