Chapter 12: Q 21. (page 916)
In Exercise, provide a rough sketch of the graph of a function of two variables with the specified level 鈥渃urve(s).鈥
All of the level curves are squares.
Short Answer

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Chapter 12: Q 21. (page 916)
In Exercise, provide a rough sketch of the graph of a function of two variables with the specified level 鈥渃urve(s).鈥
All of the level curves are squares.

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Extrema: Find the local maxima, local minima, and saddle points of the given functions.
Describe the meanings of each of the following mathematical expressions:
Construct examples of the thing(s) described in
the following.
Try to find examples that are different than
any in the reading.
(a) A function z = f(x, y) for which 鈭噁(0, 0) = 0 but f is
not differentiable at (0, 0).
(b) A function z = f(x, y) for which 鈭噁(0, 0) = 0 for every
point in R2.
(c) A function z = f(x, y) and a unit vector u such that
Du f(0, 0) = 鈭噁(0, 0) 路 u.
In Exercises, by considering the function subject to the constraint you will explore a situation in which the method of Lagrange multipliers does not provide an extremum of a function.
Why does the method of Lagrange multipliers fail with this function?
Solve the exact differential equations in Exercises 63鈥66.
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