First slide

Differentiability

Question

$The set of points where f (x) =$ $(x - 1)^{2} (x + | x - 1 |) is thrice$ $differentiable, is$

Moderate

A

R
B

$R - {0}$
C

$R - {1}$
D

$R - {0, 1}$

Solution

$\begin{array}{l} Since | x | is not diff. at x = 0 \\ \Rightarrow | x - 1 | is not diff at x = 1 . \\ x^{n} | x | is n times diff. at x = 0 \\ ∴ {(x - 1)}^{2} | x - 1 | is twice diff. at x = 1 but not thrice diff. at x = 1 \end{array}$

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