Identify the open intervals where the function is increasing or decreasing.
A) decreasing: ; increasing:
B) increasing: ; decreasing:
C) increasing: ; decreasing:
D) increasing: ; decreasing:
E) decreasing for all x

Question

​Identify the open intervals where the function  is increasing or decreasing. ​
A) ​decreasing: ; increasing: 
B) ​increasing: ; decreasing: 
C) ​increasing: ; decreasing: 
D) ​increasing: ; decreasing: 
E) ​decreasing for all x

Quizplus · Accepted Answer

To determine where a function is increasing or decreasing, we need to find the intervals where the derivative is positive (increasing) or negative (decreasing). Taking the derivative of the given function, we get:
11ea8970_69b0_5e80_861b_8578a704b81b_TB1301_11
Now we need to find where this derivative is positive or negative. Factoring the derivative, we get:
11ea8970_69b0_105e_861b_87e98c8edf32_TB1301_11
We can see from this that the derivative is positive when x < -1 or x > 1, and negative when -1 < x < 1. Therefore, the original function is increasing on the intervals (-infinity, -1) and (1, infinity), and decreasing on the interval (-1, 1). This matches choice B.

​Identify the Open Intervals Where the Function Is Increasing

Identify the Open Intervals Where the Function Is Increasing