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

If f:RR is a twice differentiable function such that f′′(x)>0 for all xR, and f(12)=12, f(1)=1, then

A
f(1)>1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
f(1)0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
12<f(1)1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
0<f(1)12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B f(1)>1
Since f′′(x)>0f(x) is increasing.
Using LMVT, There exists c such that 12<c<1 and
f(c)=f(1)f(12)112=112112=1
It is given that f′′(x)>0, hence f(x) is an increasing function.
Since f(x) is increasing and c<1
then f(1)>f(c)
Therefore f(1)>1
Hence, option A is correct.

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