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

A differentiable function f(x) will have a local minimum at x = b if -


A

f’(b) = 0 , f’(b-h) < 0 & f’(b+h) > 0

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

f’(b) = 0 , f’(b-h) > 0 & f’(b+h) < 0

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

f’(b) = 0

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 A

f’(b) = 0 , f’(b-h) < 0 & f’(b+h) > 0


We saw that if a function f(x) has a local maximum at x = c, then f’(c) = 0 , f’(c-h) > 0 & f’(c+h) < 0 . Similarly if x =b is a local minimum, then the derivative f’(b) will be zero. This is same as saying the slope of the tangent at x =b will be zero, which is clear from the figure. Now the sign of f’(x) on the left of b will be negative and on the right it will be positive.

So, we can say f’(b) = 0 , f’(b-h) < 0 & f’(b+h) > 0


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