Question

To find the critical numbers of the function f(x)=n3/3(7−x), you need to take the derivative of f(x), set it equal to zero, and solve for x. The critical numbers are the values of x where the derivative is zero or undefined.

Answer 1

The student's question is about finding the critical numbers of a function by differentiating and solving the resulting equation. It also touches on the concept of using a regression line for prediction in statistics, which relies on understanding the significance of the correlation coefficient and other related values.

Step-by-step explanation:

The question involves finding critical numbers of a given mathematical function by taking its derivative. To find these critical numbers, we need to follow a few steps:

1. Take the derivative of the function f(x) = n^3/3(7 − x).
2. Set the derivative equal to zero to find the values for x that correspond to horizontal tangents.
3. Solve for x, considering also the points where the derivative might be undefined, as these could be critical points as well.

The concept of a regression line, such as ŷ = -173.51 + 4.83x, is related but not directly connected to this problem. The regression line is useful in statistics for making predictions about one variable based on the value of another. For example, the final exam score (dependent variable y) can be predicted using the third exam score (independent variable x).

Finding critical values is also relevant to a regression analysis because it involves determining the significance of the correlation coefficient, which in turn affects whether the regression model is suited for predictions. The sample size n, and the correlation coefficient r play a significant role in these determinations.