Question

Let $f\left(x\right)=|x^2-6|x|+5|,$ then which of the following is/are correct?

• A. The number of point of non-differentiability is $3$
• B. The number of point of non-differentiability is $5$
• C. The number of integral values of $k$ for which $f\left(x\right)=k$ has exactly four solution, is $0$
• D. The number of integral values of $k$ for which $f\left(x\right)=k$ has exactly eight solution, is $3$

Answer 1

Answer: (B), (D)

The correct options are
B The number of point of non-differentiability is $5$
D The number of integral values of $k$ for which $f\left(x\right)=k$ has exactly eight solution, is $3$


Clearly, the number of points of non differentiability are 5.

The lines $y=1,y=2$ and $y=3$ cut the given curve at $8$ points.
Therefore, the number of integral values of $k$ for which $f\left(x\right)=k$ has exactly eight solution, is $3$
For $k=0,f\left(x\right)=k$ has four solutions.