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

Let f:RR be differentiable at cR and f(c)=0. If g(x)=|f(x)|, then at x=c,g is :

A
differentiable if f(c)0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
differentiable if f(c)=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
not differentiable if f(c)=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
not differentiable
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B differentiable if f(c)=0
g(x)=|f(x)|g(c)=limxc|f(x)|f(c)xc=±f(c)
and
g(c+)=limxc+|f(x)|f(c)xc=±f(c)

For g(x) to be differentiable at x=c.
R.H.D=L.H.D i.e., g(c)=g(c+)
So, f(c) must be 0, else it is non-differentiable.

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