CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The total number of local maxima and local minima of the function f(x)={(2+x)3,3<x1x23,1<x<2 is

A
2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 2
We have,
f(x)={(2+x)3,3<x1x23,1<x<2

f(x)=3(x+2)2.3<x123x13;1<x<2


Clearlyf(x) changes its sign at x=1 from +ve to –ve and so f(x) has local maxima at x=1.

lso f(0) does not exist but f(0)<0 and f(0+)>0 , it can only be inferred that f(x) has a possibility of a minima at x=0.

Hence the given function has one local maxima at x=1 and one local minima at x=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