9c How would you describe the rate of
decrease of the function?

Imagine you’re on a rollercoaster that starts off going down steeply but gradually levels out as you go along—this is akin to a function that decreases at a slower rate. In mathematical terms, this often relates to a concave up graph where the slope of the tangent line gets shallower as x increases. On the flip side, think about a slippery slide that gets steeper—this symbolizes a function decreasing at a faster rate, often found in concave down graphs where the slope becomes more negative.

When trying to determine how a function behaves as it decreases, check the derivative! Remember, if the derivative is positive but decreasing, the function is dropping at a slower pace. If the derivative is negative and becoming more negative, it signifies an increasing rate of decrease. A common mistake is not noticing these changes in slopes or overlooking the concavity, which can completely change the interpretation of the function’s behavior!