Question

The set of points where f(x) = (x–1)² (x + | x –1 | ) is thrice differentiable, is

(a)  R

(b)  R – {0}

(c)  R – {1}

(d)  R–{0,1}

Answer 1

Correct option c) R – {1}

Explanation:

Since | x | is not diff. at x = 0

⇒ | x -1| is not diff at x = 1.

xⁿ | x | n in n times diff. at x = 0

(x 1)² |x -1| 2 

⇒is twice diff. at x = 1

but not thrice diff. at x = 1