$\text { For the function } f ( x ) = ( x - 1 ) ^ { \frac { 2 } { 3 } } \text { : }$

Multiple Choice

$\text { For the function } f ( x ) = ( x - 1 ) ^ { \frac { 2 } { 3 } } \text { : }$
(a) Find the critical numbers of f (if any) ;
(b) Find the open intervals where the function is increasing or decreasing; and
(c) Apply the First Derivative Test to identify all relative extrema. Use a graphing utility to confirm your results.

A)
(a) $x = 0$
(b) increasing: $( - \infty , 0 )$ ; decreasing: $( 0 , \infty )$
(c) relative max: $f ( 0 ) = 1$
B)
(a) $x = 1$
(b) increasing: $( - \infty , 1 )$ ; decreasing: $( 1 , \infty )$
(c) relative max: $f ( 1 ) = 0$
C)
(a) $x = 1$
(b) decreasing: $( - \infty , 1 )$ ; increasing: $( 1 , \infty )$
(c) relative min: $f ( 1 ) = 0$
D)
(a) $x = 0,1$
(b) decreasing: $( - \infty , 0 ) \cup ( 1 , \infty )$ ; increasing: $( 0,1 )$
(c) relative min: $f ( 0 ) = 1$ ; relative max: $f ( 1 ) = 0$
E)
(a) $x = 0$
(b) decreasing: $( - \infty , 0 )$ ; increasing: $( 0 , \infty )$
(c) relative min: $f ( 0 ) = 1$