91Ó°ÊÓ

The minimum hourly wage in the United States has grown over the years, as shown in the table below. $$ \begin{array}{c|c} \begin{array}{c} \text { NUMBER OF YEARS, } x, \\ a) For the data in the table, find the regression line, \(y=m x+b\) b) Use the regression line to predict the minimum hourly wage in 2020 and \(2025 .\) \text { SINCE } 1997 \end{array} & \begin{array}{c} \text { MINIMUM HOURLY WAGE } \\ \text { (dollars) } \end{array} \\ \hline 0 & \$ 5.15 \\ 10 & 5.85 \\ 11 & 6.55 \\ 12 & 7.25 \\ 18 & 10.10 \end{array} $$

Evaluate. $$ \int_{0}^{2} \int_{0}^{x} e^{x+y} d y d x $$

Find the extremum of \(f(x, y)\) subject to the given constraint, and state whether it is a maximum or a minimum. $$ f(x, y, z)=x^{2}+y^{2}+z^{2} ; x+y+z=2 $$

Find the relative maximum and minimum values. $$ f(x, y)=4 y+6 x-x^{2}-y^{2} $$

Ticket prices for NFL football games have experienced steady growth, as shown in the table below. $$ \begin{array}{c|c} \begin{array}{c} \text { NUMBER OF YEARS, } x, \\ \text { SINCE } 2009 \end{array} & \begin{array}{c} \text { AVERAGE TICKET PRICE } \\ \text { (dollars) } \end{array} \\ \hline 0 & \$ 73.18 \\ 1 & 76.47 \\ 2 & 77.36 \\ 3 & 79.09 \\ 4 & 81.54 \end{array} $$ a) Find the regression line, \(y=m x+b\). b) Use the regression line to predict the average ticket price for an NFL game in 2020 and 2025

Determine the domain of each function of two variables. $$ g(x, y)=\ln \left(x^{2}-y\right) $$

Find \(f_{x}\) and \(f_{y}\). $$f(x, y)=e^{2 x-y}$$

Find \(f_{x}\) and \(f_{y}\). $$f(x, y)=e^{x y}$$

Evaluate. $$ \int_{0}^{1} \int_{1}^{e^{x}} \frac{1}{y} d y d x $$

Find the relative maximum and minimum values. $$ f(x, y)=4 x^{2}-y^{2} $$