Final answer:
To find decreasing intervals on a graph, consider the function's positivity, negative derivative, intersection points, and positive second derivative.
Step-by-step explanation:
To find decreasing intervals on a graph, we need to consider four different aspects:
A) Where the function is positive: In this case, we look for the parts of the graph where the y-values are greater than zero. These are the intervals where the function is increasing, not decreasing.
B) Where the derivative is negative: The derivative represents the rate of change of the function. A negative derivative means the function is decreasing. So, we look for intervals where the derivative is negative.
C) At points of intersection: Points of intersection occur when two functions intersect each other. We can find decreasing intervals at these points by examining the behavior of the functions around the intersection.
D) Where the second derivative is positive: The second derivative represents the concavity of the function. A positive second derivative means the function is concave upward, which implies that it is increasing. So, we look for intervals where the second derivative is positive.