The number of critical points of `f(x)=(|x-1|-1)/(x^2)`is

Options

A. 1
B. 2
C. 3
D. none of these

Answer

C

Explanation

We have
`f(x)=|x-1|/x^2={{:((x-1)/x^2","xge1),((x-2)/x^2","xlt1):}`
Clerly f(x) is not differntable at x=0 and x=1
So , by definition , these are two of the critical points other than these two ,, we have
`f(X)={{:((-x+2)/x^3", "xgt1),((x-2)/x^2", "xlt1):}`
Clearly ,f'(x)=0 at x=2 . So x=2 is also a critical poins
Hence f(x) has three critical points viz.0,1 and 2.