Let f(x, y) = x² + y² and consider the constraint 2x + 3y = 6. (a) Find a path r(t) = (x(t), y(t)) whose graph is the same as 2x + 3y = 6. (b) Find the critical point of f(r(t)). Is this point a local maximum or local minimum? (c) What we have done in parts a and b is optimize f relative to the given constraint. Using the method of Lagrange Multipliers, verify that your answer to part b is correct.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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8. Let f(x, y) = x² + y² and consider the constraint 2x + 3y = 6.
(a) Find a path r(t)
(x(t), y(t)) whose graph is the same as 2x + 3y = 6.
(b) Find the critical point of f(r(t)). Is this point a local maximum or local
minimum?
(c) What we have done in parts a and b is optimize f relative to the given
constraint. Using the method of Lagrange Multipliers, verify that your
answer to part b is correct.
Transcribed Image Text:8. Let f(x, y) = x² + y² and consider the constraint 2x + 3y = 6. (a) Find a path r(t) (x(t), y(t)) whose graph is the same as 2x + 3y = 6. (b) Find the critical point of f(r(t)). Is this point a local maximum or local minimum? (c) What we have done in parts a and b is optimize f relative to the given constraint. Using the method of Lagrange Multipliers, verify that your answer to part b is correct.
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