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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....
(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...
(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
2) Draw a contour diagram for a function f(x, y) such that at the point (, y) (0,0),
this was the information that was provided to us.
2) Draw a contour diagram for a function f(x, y) such that at the point (, y) (0,0),
2) Draw a contour diagram for a function f(x, y) such that at the point (, y) (0,0),
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
cal 3. answer a-f please. Some of the gradient vectors of a smooth function shown in...
cal 3. answer a-f please.
Some of the gradient vectors of a smooth function shown in the diagram to the right. g(x, y) are a. 3 pts At which of the points where the gradient is shown does g have the greatest rate of change? 2 b. 3 pts What is the rate of change of g at the point in part a? 2 2 -1 c. 4 pts Does g (1,0) appear to be positive, negative, or zero? Explain....
(1 point) Determine the sign of fe and fy at each indicated point using the contour diagram of shown below. (The point P is that in the first quadrant, at a positive z and y value; Q through T are lo...
(1 point) Determine the sign of fe and fy at each indicated point using the contour diagram of shown below. (The point P is that in the first quadrant, at a positive z and y value; Q through T are located clockwise from P, so that Q is at a positive r value and negative y. etc.) 6 2 P 8 (a) At point Q f is? and fy is (b) At point R is and fy is (c) At...
For the function f(x,y,z)==xyz and the point P=(-1, 8, 2): a) Calculate the gradient at P....
For the function f(x,y,z)==xyz and the point P=(-1, 8, 2): a) Calculate the gradient at P. Vf(-1, 8, 2) = b) Find the rate of change in the direction v=(2, 2, - 1) at P. D.f(-1, 8, 2)= c) Find the maximum rate of change of f at P. MAX RATE OF CHANGE =
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...
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1...
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1, 2). Find the gradient of f at the point P and draw the gradient vector on the level curve (ii) Draw the graph of f showing the level curve in (i) on the graph (iii) Explain why the function f admits a global minimum over the rectangle 0 x 2, y 1. Determine the minimum value and...
Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that is defined on a region D that contains C and f(x,y) < M for all (x, y) E D. Show that f(x, y)ds 3 Me Hint: Use...
Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that is defined on a region D that contains C and f(x,y) < M for all (x, y) E D. Show that f(x, y)ds 3 Me Hint: Use the following fact from single variable calculus: If f(x) g(x) for a KrS b, then (x)dJ() dr.
Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that...
(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...
(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
this was the information that was provided to us.
2) Draw a contour diagram for a function f(x, y) such that at the point (, y) (0,0),
2) Draw a contour diagram for a function f(x, y) such that at the point (, y) (0,0),
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
cal 3. answer a-f please.
Some of the gradient vectors of a smooth function shown in the diagram to the right. g(x, y) are a. 3 pts At which of the points where the gradient is shown does g have the greatest rate of change? 2 b. 3 pts What is the rate of change of g at the point in part a? 2 2 -1 c. 4 pts Does g (1,0) appear to be positive, negative, or zero? Explain....
(1 point) Determine the sign of fe and fy at each indicated point using the contour diagram of shown below. (The point P is that in the first quadrant, at a positive z and y value; Q through T are located clockwise from P, so that Q is at a positive r value and negative y. etc.) 6 2 P 8 (a) At point Q f is? and fy is (b) At point R is and fy is (c) At...
For the function f(x,y,z)==xyz and the point P=(-1, 8, 2): a) Calculate the gradient at P. Vf(-1, 8, 2) = b) Find the rate of change in the direction v=(2, 2, - 1) at P. D.f(-1, 8, 2)= c) Find the maximum rate of change of f at P. MAX RATE OF CHANGE =
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...
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1, 2). Find the gradient of f at the point P and draw the gradient vector on the level curve (ii) Draw the graph of f showing the level curve in (i) on the graph (iii) Explain why the function f admits a global minimum over the rectangle 0 x 2, y 1. Determine the minimum value and...
Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that is defined on a region D that contains C and f(x,y) < M for all (x, y) E D. Show that f(x, y)ds 3 Me Hint: Use the following fact from single variable calculus: If f(x) g(x) for a KrS b, then (x)dJ() dr.
Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that...
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