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Chapter 12: Q. 28 (page 976)
In Exercises 27鈥�30, use the result from Example 4 to find the distance from the point P to the given plane.
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In Exercises, find the maximum and minimum of the function f subject to the given constraint. In each case explain why the maximum and minimum must both exist.
Gradients: Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.
f(x, y ,z) = ln(x + y + z), P = (e, 0, 鈭�1) .
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?
In Exercises, find the maximum and minimum of the function f subject to the given constraint. In each case explain why the maximum and minimum must both exist.
when
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.
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