1. **Problem Statement:** Identify the local maxima and minima points from the contour plot of the function $f(x,y)$, list their coordinates and function values, and determine if any are global extrema within the shown region. 2. **Understanding Contour Plots:** Contour lines represent points where the function $f(x,y)$ has constant values. Closed contour lines indicate local maxima or minima. 3. **Given Data:** - Two circular contour regions centered near $(2,10)$ and $(6,5)$. - Function values inside these circles are approximately 10 and 9 respectively. - Contour values range from 6 to 11. 4. **Identifying Local Extrema:** - The point near $(2,10)$ with $f(2,10) = 10$ is a local maximum because the contour values decrease outward. - The point near $(6,5)$ with $f(6,5) = 9$ is a local minimum because the contour values increase outward. 5. **Listing Points in Increasing Order of $x$:** - Local maximum: $(2,10)$ with $f=10$ - Local minimum: $(6,5)$ with $f=9$ 6. **Global Extrema Check:** - The local maximum at $(2,10)$ with value 10 is the highest contour value in the region, so it is also the global maximum. - The local minimum at $(6,5)$ with value 9 is not the lowest contour value (since contours go down to 6), so it is not a global minimum. **Final Table:** | Point Type | $x$ | $y$ | $f(x,y)$ | |----------------|-----|-----|----------| | Local Maximum | 2 | 10 | 10 | | Local Minimum | 6 | 5 | 9 |