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Chapter 12: Q. 24 (page 953)
In Exercises 21-28, find the directional derivative of the given function at the specified point \(P\) and in the direction of the given unit vector \(\mathbf{u}\).
a
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Consider the function f(x, y) = 2x + 3y.
(a) Why is the graph of f a plane?
(b) In what direction is f increasing most rapidly at the
point (鈭�1, 4)?
(c) In what direction is f increasing most rapidly at the
point (x 0, y 0)?
(d) Why are your answers to parts (b) and (c) the same?
In Exercises 21鈥�26, find the discriminant of the given function.
.
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.
Use Theorem 12.32 to find the indicated derivatives in Exercises 21鈥�26. Express your answers as functions of a single variable.
Sketch the level curves f(x, y) = c of the following functions for c = 鈭�3, 鈭�2, 鈭�1, 0, 1, 2, and 3:
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