Over what interval is the graph of the function decreasing?

To determine where a function is decreasing, you'll want to find its critical points by setting the derivative equal to zero or identifying where it's undefined. Once you locate these points, you can test intervals around them using a sign chart. If the derivative is negative on an interval, then the function is decreasing there. Remember, visualizing the graph can help a lot—sometimes, the declining slope can reveal more than just numbers on paper! For practical purposes, if you have a specific function, you can also plug in values from different intervals into the derivative to confirm your findings. Common mistakes include forgetting to check endpoints or misinterpreting signs. Always double-check your calculations to ensure you haven’t missed any potential intervals where the graph could be decreasing!