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Consider the following function. f(x) = (x+2)2(x−1) (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) x = (b) Find the open intervals on which the function is increasing or decreasing. (Select all that apply. ) Increasing: (−∞, −2) (−2, 0) (0, ∞) (−∞, ∞) Decreasing: (−∞, −2) (−2, 0) (0, ∞) (−∞, ∞) (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = ( ) relative minimum (x, y) = ( ) (d) Use a graphing utility to confirm your results.

Consider the following function. f(x) = (x+2)2(x−1) (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) x = (b) Find the open intervals on which the function is increasing or decreasing. (Select all that apply. ) Increasing: (−∞, −2) (−2, 0) (0, ∞) (−∞, ∞) Decreasing: (−∞, −2) (−2, 0) (0, ∞) (−∞, ∞) (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = ( ) relative minimum (x, y) = ( ) (d) Use a graphing utility to confirm your results.

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Consider the following function.
f ( x ) = ( x + 2 ) 2 ( x − 1 )
(a) Find the critical numbers of f . (Enter your answers as a comma-separated list.)
x =
(b) Find the open intervals on which the function is increasing or decreasing. (Select all that apply.) Increasing: ( − ∞ , − 2 ) ( − 2 , 0 ) ( 0 , ∞ ) ( − ∞ , ∞ )
Decreasing: ( − ∞ , − 2 ) ( − 2 , 0 ) ( 0 , ∞ ) ( − ∞ , ∞ ) (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum ( x , y ) = ( ◻ ) relative minimum ( x , y ) = ( ◻ ) (d) Use a graphing utility to confirm your results.

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