Question

Find the intervals where the function is increasing and decreasing.

a) Increasing: (-[infinity], a), Decreasing: (a, [infinity])
b) Increasing: (a, [infinity]), Decreasing: (-[infinity], a)
c) Increasing: (-[infinity], a), Decreasing: (a, [infinity])
d) Increasing: (a, [infinity]), Decreasing: (-[infinity], a)

Answer 1

To find the intervals where a function is increasing and decreasing, analyze the slope. Option c) Increasing: (-∞, a), Decreasing: (a, ∞).

Step-by-step explanation:

To find the intervals where a function is increasing and decreasing, we need to analyze the slope of the function.

If the slope of the function is positive, the function is increasing. If the slope is negative, the function is decreasing. If the slope is zero, the function is neither increasing nor decreasing.

In this case, part A has a downward slope, so it is decreasing. Part B has an upward slope that levels off at zero, so it is increasing. Part C has an upward slope that increases in magnitude until it becomes a positive constant, so it is also increasing.

Therefore, the correct answer is option c) Increasing: (-∞, a), Decreasing: (a, ∞).