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Problem 6. (1 point) Use the contour diagram of f in the ligure below to decide...
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) 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...
Directional Derivatives
Use the contour diagram of f to decide if the specified directional derivative is positive, negative, or approximately zero.1. At the point (1,0) in the direction of −j⃗ ,2. At the point (−1,1) in the direction of (−i⃗ +j⃗ )/2√,3. At the point (−1,1) in the direction of (−i⃗ −j⃗ )/2√,4. At the point (0,2) in the direction of j⃗ ,5. At the point (−2,2) in the direction of i⃗ ,6. At the point (0,−2) in the direction of (i⃗...
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...
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)
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given ...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
I'm having trouble with b and e 46. Use the portion of the contour diagram of f(x,) shown below to estimate the following: 80 78 76 74 72 113 6 9 12 15 18 21 24 (b) f (15,76) in the direct...
I'm having trouble with b and e
46. Use the portion of the contour diagram of f(x,) shown below to estimate the following: 80 78 76 74 72 113 6 9 12 15 18 21 24 (b) f (15,76) in the direction -i+j (d) vf di where C is the path from (15,76) to (24,76) (a) gradf (15, 78) (c) A critical point of f(x, y). (e) f(x,y)dA where R is the rectangle 9Sxs 15, 76 3 y s 80...
(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
Answer the following questions for the given contour diagram of f(x, y) below: a. Estimate ∇f(4,...
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 >
17 1 아 IT 2p | 1b 1 1 19 2p | g + 이
please circle the answer! (1 point) Suppose f (x, y) = , P = (1, 3)...
please circle the answer!
(1 point) Suppose f (x, y) = , P = (1, 3) and v 3i - 2j A. Find the gradient of f Vf = i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (Vf) (P) it j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf...
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) 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...
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...
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)
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
I'm having trouble with b and e
46. Use the portion of the contour diagram of f(x,) shown below to estimate the following: 80 78 76 74 72 113 6 9 12 15 18 21 24 (b) f (15,76) in the direction -i+j (d) vf di where C is the path from (15,76) to (24,76) (a) gradf (15, 78) (c) A critical point of f(x, y). (e) f(x,y)dA where R is the rectangle 9Sxs 15, 76 3 y s 80...
(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
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 >
17 1 아 IT 2p | 1b 1 1 19 2p | g + 이
please circle the answer!
(1 point) Suppose f (x, y) = , P = (1, 3) and v 3i - 2j A. Find the gradient of f Vf = i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (Vf) (P) it j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf...
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