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

Let f(x)=x26x+5 and m is the number of points of non-derivability of y=|f(|x|)|. If |f(|x|)|=k,kR has at least m distinct solution(s), then the number of integral values of k is

A
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 4
Given : f(x)=x26x+5=(x1)(x5)
Vertex of the parabola
=(b2a,D4a)=(3,4)
The graph of y=|f(|x|)|=|(|x|1)(|x|5)| is


Clearly, y=|f(|x|)| is non-derivable at 5 points.
For |f(|x|)|=k to have at least 5 solutions,
0<k4

Hence, the number of integral values of k is 4.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction to Differentiability
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon