Let f (x, y ) be a function and fxx = x + y, D (x, y ) = fxx fyy - fxy fxy = x - 3y2 . Then what is true for the critical points P (2 ,1 ) and Q ( 1, - 4 )? O a. P and Q are both local maximum. O b. P is local maximum, Q is local minimum. O C. P and Q are both local minimum. O d. P and Q are both saddle points.

Elementary Linear Algebra (MindTap Course List)
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Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 78E: Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from...
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Зу2. Then
Let f (x, y ) be a function and fxx = x + y, D ( x, y ) = fxx fyy - fxy fxy = X -
what is true for the critical points P (2 ,1 ) and Q ( 1, - 4 )?
a. P and Q are both local maximum.
O b. P is local maximum, Q is local minimum.
O C. P and Q are both local minimum.
O d. P and Q are both saddle points.
Transcribed Image Text:Зу2. Then Let f (x, y ) be a function and fxx = x + y, D ( x, y ) = fxx fyy - fxy fxy = X - what is true for the critical points P (2 ,1 ) and Q ( 1, - 4 )? a. P and Q are both local maximum. O b. P is local maximum, Q is local minimum. O C. P and Q are both local minimum. O d. P and Q are both saddle points.
Let f (x, y, z) be a function with gradient vector < 2x, 4y, 4z > .
What is the point of extreme value of f with the constraint x + y+ z = 4?
O a. (1, -1, 4)
O b. (1, 1, 1)
О с. (2, -2, 4)
O d. (1, 2, 2)
Ое. ( 2, 1, 1)
Transcribed Image Text:Let f (x, y, z) be a function with gradient vector < 2x, 4y, 4z > . What is the point of extreme value of f with the constraint x + y+ z = 4? O a. (1, -1, 4) O b. (1, 1, 1) О с. (2, -2, 4) O d. (1, 2, 2) Ое. ( 2, 1, 1)
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