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Chapter 12: Q 14 (page 975)
Use Theorem to show that the point
The point
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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 ∇f(0, 0) = 0 but f is
not differentiable at (0, 0).
(b) A function z = f(x, y) for which ∇f(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) = ∇f(0, 0) · u.
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
Sketch the level curves f(x, y) = c of the following functions for c = −3, −2, −1, 0, 1, 2, and 3:
Partial derivatives: Find all first- and second-order partial derivatives for the following functions:
Explain the steps you would take to find the extrema of a function of two variables, is a point in the rectangle defined by role="math" localid="1649881836115"
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