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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Suppose a point P lies on the curve g(x, y) = c. Let ủg # 0 be the tangent
vector to that curve at the point P. Suppose that for a differentiable function
f(x, y), its gradient at P is nonzero and orthogonal to ug. Then...
[select one answer in the first three options, and one more in the second three
options]
O P must be the location of an extremum for f (x, y) subject to the constraint
g (x, y) = c.
= C.
O P may or may not be the location of an extremum for f (x, y) subject to the constraint
g (x, y) = c.
= C.
O P must not be the location of an extremum for f (x, y) subject to the constraint
g (x, y) = c.
The directional derivative f (P) equals zero.
Ug
O The directional derivative f>(P) does not equal zero.
Ug
The directional derivative f→(P) may or may not equal zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb3cf4b8-b456-4664-9286-f23170705135%2Febd381da-5bba-477f-a454-828cc0828c4c%2Fsoavgud_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose a point P lies on the curve g(x, y) = c. Let ủg # 0 be the tangent
vector to that curve at the point P. Suppose that for a differentiable function
f(x, y), its gradient at P is nonzero and orthogonal to ug. Then...
[select one answer in the first three options, and one more in the second three
options]
O P must be the location of an extremum for f (x, y) subject to the constraint
g (x, y) = c.
= C.
O P may or may not be the location of an extremum for f (x, y) subject to the constraint
g (x, y) = c.
= C.
O P must not be the location of an extremum for f (x, y) subject to the constraint
g (x, y) = c.
The directional derivative f (P) equals zero.
Ug
O The directional derivative f>(P) does not equal zero.
Ug
The directional derivative f→(P) may or may not equal zero.
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