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For the Function : (A) Find the Critical Numbers

Question 33

Multiple Choice

For the function For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. : (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.
Then use a graphing utility to confirm your results.


A) (a) x = 0 , 4 (b) increasing: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. ; decreasing: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. (c) relative max: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. ; relative min: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min.
B) (a) x = 0 , 4 (b) decreasing: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. ; increasing: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. (c) relative min: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. ; relative max: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min.
C) (a) x = 0 , 1 (b) increasing: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. ; decreasing: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. (c) relative max: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. ; relative min: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min.
D) (a) x = 0 , 1 (b) decreasing: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. ; increasing: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. (c) relative min: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. ; relative max: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min.
E) (a) x = 0 , 1 (b) increasing: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. ; decreasing: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. (c) relative max: For the function : (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. Then use a graphing utility to confirm your results. A) (a) x = 0 , 4 (b) increasing: ; decreasing: (c) relative max: ; relative min: B) (a) x = 0 , 4 (b) decreasing: ; increasing: (c) relative min: ; relative max: C) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; relative min: D) (a) x = 0 , 1 (b) decreasing: ; increasing: (c) relative min: ; relative max: E) (a) x = 0 , 1 (b) increasing: ; decreasing: (c) relative max: ; no relative min. ; no relative min.

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