Question

Let be a function that is decreasing for ______ and decreasing for ______. If ______, which of the following could represent the function?

Answer 1

The function that has a positive value and a positive slope that decreases in magnitude with increasing x at x = 3 is y = x².

Step-by-step explanation:

Regarding the function in question, when looking at x = 3, the description given is that of f(x) having a positive value with a positive slope that is decreasing in magnitude with increasing x. This means as x increases beyond 3, the slope of the function is getting less steep. Considering the choices, option (b) y = x² is the function that fits the given conditions. This is because the derivative of y = x² is y' = 2x, which indeed is positive at x = 3 and decreases in magnitude as x increases.