Chapter 12: Q 14. (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
One level curve consists of exactly two points.
Short Answer

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Chapter 12: Q 14. (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
One level curve consists of exactly two points.

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In Exercises , use the partial derivatives of and the point specified to
find the equation of the line tangent to the surface defined by the function in the direction,
find the equation of the line tangent to the surface defined by the function in the direction, and
find the equation of the plane containing the lines you found in parts and .
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.
Optimize subject to the constraint for nonzero constants a and b. Are there any nonzero values of a and b for which the method of Lagrange multipliers succeeds?
Describe the meanings of each of the following mathematical expressions:
When you use the method of Lagrange multipliers to find the maximum and minimum of subject to the constraint you obtain two points. Is there a relative maximum at one of the points and a relative minimum at the other? Which is which?
Solve the exact differential equations in Exercises 63鈥66.
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