turkey-yks 2015 Q40

turkey-yks · Other · lys1-math Modulus function Differentiability of functions involving modulus

I. $f ( x ) = x - 1$ II. $g ( x ) = | x - 1 |$ III. $h ( x ) = \sqrt [ 3 ] { ( x - 1 ) ^ { 2 } }$ Which of the following functions do not have a derivative at the point $x = 1$?
A) Only I
B) Only II
C) I and II
D) II and III
E) I, II and III

I. $f ( x ) = x - 1$\\
II. $g ( x ) = | x - 1 |$\\
III. $h ( x ) = \sqrt [ 3 ] { ( x - 1 ) ^ { 2 } }$\\
Which of the following functions do not have a derivative at the point $x = 1$?\\
A) Only I\\
B) Only II\\
C) I and II\\
D) II and III\\
E) I, II and III

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