Question

Use an increasing and decreasing intervals calculator for a given function.

A) Interval I: (-[infinity], -2), Interval II: (-2, [infinity])
B) Interval I: (-[infinity], 2), Interval II: (2, [infinity])
C) Interval I: (-[infinity], 0), Interval II: (0, [infinity])
D) Interval I: (-[infinity], 4), Interval II: (4, [infinity])

Answer 1

The correct option is B) Interval I: (-∞, 2), Interval II: (2, ∞). The function is increasing on Interval I and decreasing on Interval II.

Step-by-step explanation:

The correct option for the given intervals is B) Interval I: (-∞, 2), Interval II: (2, ∞).

To determine whether a function is increasing or decreasing on a given interval, we can look at the slope of the function. If the slope is positive, the function is increasing, and if the slope is negative, the function is decreasing.

In this case, for Interval I (-∞, 2), the function has a positive slope, indicating it is increasing. For Interval II (2, ∞), the function has a negative slope, indicating it is decreasing.

Therefore, option B) Interval I: (-∞, 2), Interval II: (2, ∞) is the correct option.