CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

According to LMVT, if a function f(x) is continuous on [a, b] and differentiable on the interval (a, b) then which of the following option should be correct for some value c from the interval (a,b)?( c can take any value from the interval (a,b) )


A

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

No worries! We‘ve got your back. Try BYJU‘S free classes today!
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 B


LMVT theorem states that if a function f(x) is continuous on [a, b] and differentiable on the interval (a, b) then we’ll have slope of the tangent drawn at some x = c where c ∈ (a, b) equal to the slope of secant joining points (a, f(a)) & (b, f(b)). Slope of tangent at x =c is f’(c). Slope of secant is the average rate of change of f(x) over the interval [a,b]

f(C)=f(a)f(b)ab


flag
Suggest Corrections
thumbs-up
0
mid-banner-image
mid-banner-image
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
Select...
similar_icon
Related Videos
thumbnail
lock
Theorems
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
Select...