Answer the following questions for the given contour diagram of f(x, y) below:
a. Estimate ∇f(4, 1)
b. Estimate the maximum and minimum rates of change of f at the point (4, 1)
c. In two different ways, estimate the rate of change of f at the point (4, 1) in the direction of the vector < −1, 1 >
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Answer the following questions for the given contour diagram of
f(x, y) below:
a. Estimate ∇f(4,...
(1 point) A contour diagram for a function f(x,y) is shown below. 4 --- - --...
(1 point) A contour diagram for a function f(x,y) is shown below. 4 --- - -- --5 ---- - - 4 ----- Estimate the position and approximate value of the global maximum and global minimum on the region shown. Global maximum at Global minimum at
(1 point) Use the contour diagram for f(x, y) shown below to estimate the directional derivative...
(1 point) Use the contour diagram for f(x, y) shown below to estimate the directional derivative off in the direction v at the point P. (a) At the point P = (2, 2) in the direction ✓ = 7, the directional derivative is approximately O‘ot 16.0 18.0 12.0 14.0 2.0 (b) At the point P = (3, 2) in the direction ✓ = -1, the directional derivative is approximately 8.0 (c) At the point P = (4,1) in the direction...
17 marks] Consider the functionf(x, y) = (y - 1) (x- 1). (a) Find a unit normal vector to the contour line given by f=0...
17 marks] Consider the functionf(x, y) = (y - 1) (x- 1). (a) Find a unit normal vector to the contour line given by f=0.5 at the point (x,y) (1.5,2). Do not forget to check that this point is on the contour line. (b) Consider the curve L given by r(t) = 2ti+3tj with 0 ts1 and the Cartesian basis vectors i= (1,0) and j= (0,1) of R2. Determine using the chain rule and use this result to determine all...
A contour map for a function z=f(x, y) is given: Answer the following questions: Question 1....
A contour map for a function z=f(x, y) is given:
Answer the following questions:
Question 1. A contour map for a function z S(z,y) is given: -2 k-1 k-1- k-2 Answer the following questions. (a) (1 point) What is f(-1,1)? (b) (2 points) Describe the set of all points (r, y) such that f(z,y) = 0. Which of the following graphs best represents the graph of this function? (c) (1 point) B. A. D.
Question 1. A contour map for...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
Given to the right is a contour diagram for a difereatiable functionh Use the diagram to answer t...
Given to the right is a contour diagram for a difereatiable functionh Use the diagram to answer the questions that follow (a) Estimate Vh(2, 1). Clearly demonstrate what you are doing to arrive at an answer 8 12 16 20 (b) Estimate the directional derivative of h at (2, 1) in the direction of the point (4,0) 8 12 16 (c) Which appears to be larger in value, #(2.5,1.5) or J(2.5, 1.5)? Explain
Given to the right is a contour...
Answer all parts please. (calculus/contour/gradient/max/min) The figure to the right shows the contours of a smooth fun...
Answer all parts please. (calculus/contour/gradient/max/min)
The figure to the right shows the contours of a smooth function z = f(x,y) . a. 2 pes Label a point A on the contour graph where the gradient ofpoints in the same direction as-i+j. b. 2ps Label a point M on the contour graph where lgrad appears to be largest c. 4 pts Estimate the locations and values of the maximum and minimum of f(x, y) subject to the triangular constraint x+ys8, x20,...
Multivariable Calculus Question 3. (2 pts) The contour diagram for a function, f(x, y) is shown below. Estimate the length of the gradient at point P. Be sure to show or explain your reasoning. 2....
Multivariable Calculus Question
3. (2 pts) The contour diagram for a function, f(x, y) is shown below. Estimate the length of the gradient at point P. Be sure to show or explain your reasoning. 2.4 1.6 pe 0.8 0.8 1.6 2.4 24 1.60.80.8 16 24 2.4
3. (2 pts) The contour diagram for a function, f(x, y) is shown below. Estimate the length of the gradient at point P. Be sure to show or explain your reasoning. 2.4 1.6 pe...
17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find...
17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find i. the directional derivative of the function at the point P in the direction of v. ii. the maximum rate of change of f.
3. (5 pts) Use the contour diagram of f in Figure below to decide if the...
3. (5 pts) Use the contour diagram of f in Figure below to decide if the specified directional derivative is positive, negative, or approximately zero Y 3 2 1 -2 3 1 2 3 -3 -2 -1 (a) At the point (-2,2), in direction i. (b) At the point (0,-2), in direction j (c) At the point (-1,1), in direction i+j. (d) At the point (-1,1), in direction -i+ j. (e) At the point (0, -2), in direction i- 2j.
(1 point) A contour diagram for a function f(x,y) is shown below. 4 --- - -- --5 ---- - - 4 ----- Estimate the position and approximate value of the global maximum and global minimum on the region shown. Global maximum at Global minimum at
(1 point) Use the contour diagram for f(x, y) shown below to estimate the directional derivative off in the direction v at the point P. (a) At the point P = (2, 2) in the direction ✓ = 7, the directional derivative is approximately O‘ot 16.0 18.0 12.0 14.0 2.0 (b) At the point P = (3, 2) in the direction ✓ = -1, the directional derivative is approximately 8.0 (c) At the point P = (4,1) in the direction...
17 marks] Consider the functionf(x, y) = (y - 1) (x- 1). (a) Find a unit normal vector to the contour line given by f=0.5 at the point (x,y) (1.5,2). Do not forget to check that this point is on the contour line. (b) Consider the curve L given by r(t) = 2ti+3tj with 0 ts1 and the Cartesian basis vectors i= (1,0) and j= (0,1) of R2. Determine using the chain rule and use this result to determine all...
A contour map for a function z=f(x, y) is given:
Answer the following questions:
Question 1. A contour map for a function z S(z,y) is given: -2 k-1 k-1- k-2 Answer the following questions. (a) (1 point) What is f(-1,1)? (b) (2 points) Describe the set of all points (r, y) such that f(z,y) = 0. Which of the following graphs best represents the graph of this function? (c) (1 point) B. A. D.
Question 1. A contour map for...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
Given to the right is a contour diagram for a difereatiable functionh Use the diagram to answer the questions that follow (a) Estimate Vh(2, 1). Clearly demonstrate what you are doing to arrive at an answer 8 12 16 20 (b) Estimate the directional derivative of h at (2, 1) in the direction of the point (4,0) 8 12 16 (c) Which appears to be larger in value, #(2.5,1.5) or J(2.5, 1.5)? Explain
Given to the right is a contour...
Answer all parts please. (calculus/contour/gradient/max/min)
The figure to the right shows the contours of a smooth function z = f(x,y) . a. 2 pes Label a point A on the contour graph where the gradient ofpoints in the same direction as-i+j. b. 2ps Label a point M on the contour graph where lgrad appears to be largest c. 4 pts Estimate the locations and values of the maximum and minimum of f(x, y) subject to the triangular constraint x+ys8, x20,...
Multivariable Calculus Question
3. (2 pts) The contour diagram for a function, f(x, y) is shown below. Estimate the length of the gradient at point P. Be sure to show or explain your reasoning. 2.4 1.6 pe 0.8 0.8 1.6 2.4 24 1.60.80.8 16 24 2.4
3. (2 pts) The contour diagram for a function, f(x, y) is shown below. Estimate the length of the gradient at point P. Be sure to show or explain your reasoning. 2.4 1.6 pe...
17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find i. the directional derivative of the function at the point P in the direction of v. ii. the maximum rate of change of f.
3. (5 pts) Use the contour diagram of f in Figure below to decide if the specified directional derivative is positive, negative, or approximately zero Y 3 2 1 -2 3 1 2 3 -3 -2 -1 (a) At the point (-2,2), in direction i. (b) At the point (0,-2), in direction j (c) At the point (-1,1), in direction i+j. (d) At the point (-1,1), in direction -i+ j. (e) At the point (0, -2), in direction i- 2j.
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