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

Compute the value of θ in the first mean value theorem f(x+h)=f(x)+hf(x+θh) if f(x)=ax2+bx+c.

A
12
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
13
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
14
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
15
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 12
We have f(x)=ax2+bx+c.
f(x+h)=a(x+h)2+b(x+h)+c
Also, f(x)=2ax+b
f(x+θh)=2a(x+θh)+c
Putting these values in Lagrange's mean value theorem we get
f(x+h)=f(x)+hf(x+θh)a(x+h)2+b(x+h)+c=ax2+bx+c+h[2a(x+θh)+b]
when x0. we have ah2+bh+c+h[2aθh+b]
ah2=2aθh2 or θ=12
which is the required value of θ.

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