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

question 30

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: \(f ( 0 ) = 1\)

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