1. **Problem Statement:** Identify the local maxima and minima of the function $f(x,y)$ from the given contour plot data, list their coordinates and function values, and determine which are global extrema. 2. **Given Data:** - Local maxima: $f(0,0) = 14$, $f(35,35) = 12.5$ - Local minima: $f(12,30) = 7$, $f(38,18) = 6$ - Global maximum at $(0,0)$ - Global minimum at $(37,18)$ (noting the closest local minimum is at $(38,18)$ with value 6) 3. **Explanation:** - A **local maximum** is a point where the function value is higher than all nearby points. - A **local minimum** is a point where the function value is lower than all nearby points. - A **global maximum/minimum** is the highest/lowest value over the entire domain. 4. **Analysis:** - The point $(0,0)$ with $f=14$ is the highest value in the domain, so it is both a local and global maximum. - The point $(35,35)$ with $f=12.5$ is a local maximum but not global since $14 > 12.5$. - The point $(12,30)$ with $f=7$ is a local minimum but not global since $6 < 7$. - The point $(38,18)$ with $f=6$ is a local minimum and is the global minimum since it is the lowest value in the domain. 5. **Final answers:** - Local maxima: $(0,0)$ with $f=14$ (also global max), $(35,35)$ with $f=12.5$ - Local minima: $(12,30)$ with $f=7$, $(38,18)$ with $f=6$ (also global min)