wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

Let f be twice differentiable function satisfying f(1)=1,f(2)=4,f(3)=9, then

A
f′′(x)=2,xϵR
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
f(x)=5=f′′(x). For some xϵ(1,3)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
There exists atleast one xϵ(1,3) such that f′′(x)=2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
None of the above
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C There exists atleast one xϵ(1,3) such that f′′(x)=2
Let g(x)=f(x)x2
g(x) has atleast 3 real roots which are x=1,2,3 (by mean value theorem)
g(x) has atleast 2 real roots in xϵ(1,3)
g′′(x) has atleast 1 real root in xϵ(1,3)
f′′(x)=2 for atleast one xϵ(1,3).

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