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.Use a graphing utility to confirm your results.
A)(a) (b) decreasing: ; increasing: (c) relative min:
B)(a) (b) increasing: ; decreasing: (c) relative max:
C)(a) (b) decreasing: ; increasing: (c) relative min: ; relative max:
D)(a) (b) decreasing: ; increasing: (c) relative min:
E)(a) (b) increasing: ; decreasing: (c) relative max:

Question

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.Use a graphing utility to confirm your results.
A)(a) (b) decreasing: ; increasing: (c) relative min: 
B)(a) (b) increasing: ; decreasing: (c) relative max: 
C)(a) (b) decreasing: ; increasing: (c) relative min: ; relative max: 
D)(a) (b) decreasing: ; increasing: (c) relative min: 
E)(a) (b) increasing: ; decreasing: (c) relative max:

Quizplus · Accepted Answer

The critical number is found by setting the derivative equal to zero and solving for x. However, since we are not given the actual function, we cannot find the critical number(s) and determine the intervals of increase and decrease or the relative extrema. Therefore, we cannot confirm with a graphing utility either. Choice A is the only option that gives a plausible answer, but it is still based on incomplete information.

For the Function :(A) Find the Critical Numbers of F