If the IROC at x=10 is zero units/unit, at x=9 is -4 units/unit, and at x=12 is 3 units/unit explain what you know about the function and how you know it.

Answer 1

Based on the information provided about the instantaneous rate of change (IROC) of the function at different values of x, we can infer the following:

1. At x=10, the IROC is zero units/unit, which indicates that the function is not changing at that point. This implies that the function has a horizontal tangent at x=10.

2. At x=9, the IROC is -4 units/unit, which means that the function is decreasing (sloping downwards) at that point. This suggests that the function has a negative slope at x=9.

3. At x=12, the IROC is 3 units/unit, indicating that the function is increasing (sloping upwards) at that point. This implies that the function has a positive slope at x=12.

Based on these observations, we can determine that the function is likely continuous and differentiable at these points, as the IROC values provide information about the rate of change of the function. Additionally, we can infer the general trend of the function over the given interval based on the IROC values at specific points.