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3. (5 pts) Use the contour diagram of f in Figure below to decide if the...
Problem 6. (1 point) Use the contour diagram of f in the ligure below to decide...
Problem 6. (1 point) Use the contour diagram of f in the ligure below to decide ir the speciñied directional derivatives below are positive, negative, or approxmately zero 14 (a) At point (-2,2). in direction-i. is.? (b) At point (0,-2) in direction- i f s ? (c) At point ( 1,1), in direction i + s ? a) At point (-1,1), in direction +j f: s ? (e) At point (0,-2), in direction it2j. fd is!? n At point (0,-2),...
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...
(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...
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)
Question 1. (15 pts) Given f(x, y) = 3x 2 + y 3 . (a) Find...
Question 1. (15 pts) Given f(x,
y) = 3x 2 + y 3 . (a) Find the gradient of f. (b) Find the
directional derivative of f at P0 = (3, 2) in the direction of u =
(5/13)i + (12/13)j.
Question 1. (15 pts) Given f(L,y) = 3x2 +y?. (a) Find the gradient of f. (b) Find the directional derivative off at P =(3,2) in the direction of u=(5/13)i + (12/13)j.
Please help. 16, Figure 8.59 is a contour diagram for z f(x, y). Is positive or negative? Is fy positive or negative? Estimate f(2, 1), fz (2, 1), and fs(2, 1). -6 10 14 18 Figure 8.59 16, Figur...
Please help.
16, Figure 8.59 is a contour diagram for z f(x, y). Is positive or negative? Is fy positive or negative? Estimate f(2, 1), fz (2, 1), and fs(2, 1). -6 10 14 18 Figure 8.59
16, Figure 8.59 is a contour diagram for z f(x, y). Is positive or negative? Is fy positive or negative? Estimate f(2, 1), fz (2, 1), and fs(2, 1). -6 10 14 18 Figure 8.59
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at...
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at the point (1,-1,1) in the direction of ū= (1,2,3). Is there a direction û in which f(x, y, z) has a directional derivative Dof = -3 at the point (1,-1,1)?
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...
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...
Problem 6. (1 point) Use the contour diagram of f in the ligure below to decide ir the speciñied directional derivatives below are positive, negative, or approxmately zero 14 (a) At point (-2,2). in direction-i. is.? (b) At point (0,-2) in direction- i f s ? (c) At point ( 1,1), in direction i + s ? a) At point (-1,1), in direction +j f: s ? (e) At point (0,-2), in direction it2j. fd is!? n At point (0,-2),...
(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)
Question 1. (15 pts) Given f(x,
y) = 3x 2 + y 3 . (a) Find the gradient of f. (b) Find the
directional derivative of f at P0 = (3, 2) in the direction of u =
(5/13)i + (12/13)j.
Question 1. (15 pts) Given f(L,y) = 3x2 +y?. (a) Find the gradient of f. (b) Find the directional derivative off at P =(3,2) in the direction of u=(5/13)i + (12/13)j.
Please help.
16, Figure 8.59 is a contour diagram for z f(x, y). Is positive or negative? Is fy positive or negative? Estimate f(2, 1), fz (2, 1), and fs(2, 1). -6 10 14 18 Figure 8.59
16, Figure 8.59 is a contour diagram for z f(x, y). Is positive or negative? Is fy positive or negative? Estimate f(2, 1), fz (2, 1), and fs(2, 1). -6 10 14 18 Figure 8.59
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at the point (1,-1,1) in the direction of ū= (1,2,3). Is there a direction û in which f(x, y, z) has a directional derivative Dof = -3 at the point (1,-1,1)?
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...
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...
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