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Problem 10

Classify the shaded value in each table as one of the following: a. a relative maximum b. a relative minimum c. a saddle point d. neither a relative extremum nor a saddle point $$ \begin{array}{|r|r|r|r|r|r|r|} \hline & \mathbf{- 3} & \mathbf{- 2} & \mathbf{- 1} & \mathbf{0} & \mathbf{1} & \mathbf{2} \\ \hline \mathbf{- 3} & 100 & 101 & 100 & 97 & 92 & 85 \\ \hline \mathbf{- 2} & 99 & 100 & 99 & 96 & 91 & 84 \\ \hline \mathbf{- 1} & 98 & 99 & 98 & 95 & 90 & 83 \\ \hline \mathbf{0} & 91 & 92 & 91 & 88 & 83 & 76 \\ \hline \mathbf{1} & 72 & 73 & 72 & 69 & 64 & 57 \\ \hline \mathbf{2} & 35 & 36 & 35 & 32 & 27 & 20 \\ \hline \mathbf{3} & -26 & -25 & -26 & -29 & -34 & -41 \\ \hline \end{array} $$

Expert verified

The shaded value 88 in the table can be classified as neither a relative extremum nor a saddle point (option d).

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Chapter 15

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Chapter 15

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Chapter 15

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Chapter 15

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