Structural Analysis
Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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this is for a review. The second image is the answer key
![画像:[1] Answer Key (a) (3.33%)) is a saddle point; f(4,2) = 0 is a relative minimum value of f. (b) f(0,0) = 4 is a relative maximum value of f; f(2,0) = 0 is a relative minimum value of f; (1,1,f(1,1)) is a saddle point; (1,-1,f(1,-1)) is also a saddle point. [2] (a) 13 [3] w/w (b) [4] [5] (a) (20,-10). (b) The toxicity is lowest at (0,0) and (2,4). -2x+11y+10z = 34.](https://content.bartleby.com/qna-images/question/bb745e20-1e91-42b2-a546-4e64ee6df49f/390f0a07-e7c2-40ef-a05b-18e3b0c63ced/2uv6mbj_thumbnail.png){kind=link}
Transcribed Image Text:[1]
Answer Key
(a) (3.33%)) is a saddle point; f(4,2) = 0 is a relative minimum value of f.
(b) f(0,0) = 4 is a relative maximum value of f; f(2,0) = 0 is a relative minimum value of f;
(1,1,f(1,1)) is a saddle point; (1,-1,f(1,-1)) is also a saddle point.
[2]
(a)
13
[3]
w/w
(b)
[4]
[5]
(a) (20,-10).
(b) The toxicity is lowest at (0,0) and (2,4).
-2x+11y+10z = 34.
![画像:[1] For each of the following functions, find all local extrema and saddle points. (a) f(x,y) = x2-4xy+y3 +4y (b) f(x,y) = x3+3xy2-3x2-3y2+4 [2] Let f(x,y) In(y-2x+1). [3] [4] [5] (a) Sketch the domain of f. (b) Sketch the level curve of f which contains the point (1,2). Find the directional derivative of the function f(x,y,z)=3xz-2xy2 at the point (-1, 1, 2) in the direction from (-1, 1, 2) to (1, 3, 3). A spider living in a two-dimensional world finds itself in a toxic environment. The toxicity at (x,y) is given by the function T(x,y) = 4x2-4xy + y2. (a) If the spider is at the point (-2, 1), in which direction should it move in order to lower the toxicity the fastest? (b) Use Lagrange multipliers to determine the point(s) along the parabola y = x2 at which the toxicity is the lowest. Find an equation of the plane tangent to the surface xyz-4xz3+ y3 = 10 at the point (-1, 2, 1).](https://content.bartleby.com/qna-images/question/bb745e20-1e91-42b2-a546-4e64ee6df49f/390f0a07-e7c2-40ef-a05b-18e3b0c63ced/3sy1az5r_thumbnail.png){kind=link}
Transcribed Image Text:[1]
For each of the following functions, find all local extrema and saddle points.
(a) f(x,y) = x2-4xy+y3 +4y
(b) f(x,y) = x3+3xy2-3x2-3y2+4
[2]
Let f(x,y) In(y-2x+1).
[3]
[4]
[5]
(a) Sketch the domain of f.
(b) Sketch the level curve of f which contains the point (1,2).
Find the directional derivative of the function f(x,y,z)=3xz-2xy2 at the point
(-1, 1, 2) in the direction from (-1, 1, 2) to (1, 3, 3).
A spider living in a two-dimensional world finds itself in a toxic environment. The toxicity
at (x,y) is given by the function T(x,y) = 4x2-4xy + y2.
(a) If the spider is at the point (-2, 1), in which direction should it move in order to lower
the toxicity the fastest?
(b) Use Lagrange multipliers to determine the point(s) along the parabola y = x2 at
which the toxicity is the lowest.
Find an equation of the plane tangent to the surface xyz-4xz3+ y3 = 10 at the point
(-1, 2, 1).
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