Partial derivative
Let f be a plane in three dimensions. If the rate of change of f with respect to x at the point (1,2) is equal to 4 and the rate of change of f with respect to y at the point (1,2) is equal to -2, what is the rate of change of f with respect to x at the point (44,4)?
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Problem 2. Suppose that gx, y, 2) is a function with the following properties: -1,2,-4 5,...
Problem 2. Suppose that gx, y, 2) is a function with the following properties: -1,2,-4 5, 9(-1,2,-4)-2, 9u(-1,2,-4) -3, and 9.(-1,2,-4) 6 Answer the following questions, and carefully justify all your answers. (a) Estimate the value of g(-0.8,2.1,-4.2). near y (b) In what direction from the point (-1,2, -4) does g decrease the fastest? What is the rate of change in this direction? (c) Which of the following objects exist(s)? Justify your answers, and find an equation for the ones...
6. Let px -5 and Py-2. Consi 2. Consider the following equation (a) Find the partial...
6. Let px -5 and Py-2. Consi 2. Consider the following equation (a) Find the partial derivative with respect to x, and call it fr (b) Find the partial derivative with respect to y, J^ and call it fu (c) Plug in the above to get equation 1 (and simplify) Equation 1L. (d) Find 4 (x, y) points such that f(x, y) - 80 (e) Any combination of (x, y) that leads to f(x,y) 80 must satisfy what equation? Let...
6. Let px -5 and Py-2. Consi 2. Consider the following equation (a) Find the partial...
6. Let px -5 and Py-2. Consi 2. Consider the following equation (a) Find the partial derivative with respect to x, and call it fr (b) Find the partial derivative with respect to y, J^ and call it fu (c) Plug in the above to get equation 1 (and simplify) Equation 1L. (d) Find 4 (x, y) points such that f(x, y) - 80 (e) Any combination of (x, y) that leads to f(x,y) 80 must satisfy what equation? Let...
#2 #3 #4 #5 please help me with the TRUE or FALSE Given Vf(1,2, 0) =...
#2
#3
#4
#5
please help me with the TRUE or FALSE
Given Vf(1,2, 0) = 3i +j -4k, at point (1,2, 0) the directional derivative in the direction <1, 2, -2> is... 5 None of the three. 13 3 13 Considerf (x, y) xe-2* at (x, y) (1,2) Which of the following is FALSE? To estimate f(0.9, 2. 2), let dx = -0. 1 and dy 0.2, calculatedf(1,2), and subtract it from f(1,2). f(1, 2) 1 None of the...
Calculus III 1) Identify each of the following surfaces: а) z' %3x? - 5у" b) z...
Calculus III
1) Identify each of the following surfaces: а) z' %3x? - 5у" b) z 4x2-4 y c) z2+3x2-5y = 4 d) z2x23-5y e) у3х* 2) Find and classify all of the critical points for f(x, y)=xy -x2 + y'. 3) Find the maximum and minimum values of f(x,y)=xy over the ellipse х* + 2y %3D1. 4) Let fx, y) x3 -cosy a) Find the first order Taylor polynomial for f(x,y) based at (1,7). b) Find the sccond order...
Let T(x,y) denote the temperature at location (x,y). You are given the following information. • The...
Let T(x,y) denote the temperature at location (x,y). You are given the following information. • The rate of change of T at the point A(1,2) in the direction ~ w = ˆ i + ˆ j is √8. • The rate of change of T at the point A(1,2) in the direction ~ v = 4ˆ i −3ˆ j is 6. • The temperature at A(1,2) is 20. (a) From the point A(1,2), in which direction would you head to...
Assume that f(x,y) has a continuous partial derivatives and let (1,2) be a critical point. Given...
Assume that f(x,y) has a continuous partial derivatives and let (1,2) be a critical point. Given that far(1,2)=2 fy(1,2), and fx/(1,2)=fyx(1,2)= 18. If f has a saddle point at (1,2), then one of the following statements is true Select one: a. None of the choices is correct answer bif y(1,2) is less than - 3 or greater than 3 c.f xa {1,2) is less than 3 and greater than - 3 d. fxr (1,2) is less than 6 and greater...
vector calculus. Do both please Q1: What, in your own words, is the difference between a partial derivative and a di...
vector calculus.
Do
both please
Q1: What, in your own words, is the difference between a partial derivative and a directional derivative? How are they similar? Give a particular example to illustrate your explanations (choose some function z=f(x,y)) Q2: Given a surface z= f(x,y), a point (x,yo) in the domain of f, and a unit vector i pointing some direction in the xy-plane, what does it mean if D,f(x,Y)=0? Be as specific as possible.
Q1: What, in your own words,...
Question 6 10 points Save Ans Determine the partial derivative of the following function with respect...
Question 6 10 points Save Ans Determine the partial derivative of the following function with respect to "z" and evaluate at point A:(-3,4,-2): f(x, y, z) = axºyz+b yºxz+cz*yx Uses the following values: a=4; b=3; and c=1.
What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal...
What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2)? -8 -3 4 12 b) c) d) e) none of these 113 113 V13 113 a) o What is the average rate of change of z = f(x, y) = x² + xy(with respect to horizontal distance) as one travels from (2,1) to (4,-2)? 2 5 12 c) d) e) none of...
Problem 2. Suppose that gx, y, 2) is a function with the following properties: -1,2,-4 5, 9(-1,2,-4)-2, 9u(-1,2,-4) -3, and 9.(-1,2,-4) 6 Answer the following questions, and carefully justify all your answers. (a) Estimate the value of g(-0.8,2.1,-4.2). near y (b) In what direction from the point (-1,2, -4) does g decrease the fastest? What is the rate of change in this direction? (c) Which of the following objects exist(s)? Justify your answers, and find an equation for the ones...
6. Let px -5 and Py-2. Consi 2. Consider the following equation (a) Find the partial derivative with respect to x, and call it fr (b) Find the partial derivative with respect to y, J^ and call it fu (c) Plug in the above to get equation 1 (and simplify) Equation 1L. (d) Find 4 (x, y) points such that f(x, y) - 80 (e) Any combination of (x, y) that leads to f(x,y) 80 must satisfy what equation? Let...
6. Let px -5 and Py-2. Consi 2. Consider the following equation (a) Find the partial derivative with respect to x, and call it fr (b) Find the partial derivative with respect to y, J^ and call it fu (c) Plug in the above to get equation 1 (and simplify) Equation 1L. (d) Find 4 (x, y) points such that f(x, y) - 80 (e) Any combination of (x, y) that leads to f(x,y) 80 must satisfy what equation? Let...
#2
#3
#4
#5
please help me with the TRUE or FALSE
Given Vf(1,2, 0) = 3i +j -4k, at point (1,2, 0) the directional derivative in the direction <1, 2, -2> is... 5 None of the three. 13 3 13 Considerf (x, y) xe-2* at (x, y) (1,2) Which of the following is FALSE? To estimate f(0.9, 2. 2), let dx = -0. 1 and dy 0.2, calculatedf(1,2), and subtract it from f(1,2). f(1, 2) 1 None of the...
Calculus III
1) Identify each of the following surfaces: а) z' %3x? - 5у" b) z 4x2-4 y c) z2+3x2-5y = 4 d) z2x23-5y e) у3х* 2) Find and classify all of the critical points for f(x, y)=xy -x2 + y'. 3) Find the maximum and minimum values of f(x,y)=xy over the ellipse х* + 2y %3D1. 4) Let fx, y) x3 -cosy a) Find the first order Taylor polynomial for f(x,y) based at (1,7). b) Find the sccond order...
Assume that f(x,y) has a continuous partial derivatives and let (1,2) be a critical point. Given that far(1,2)=2 fy(1,2), and fx/(1,2)=fyx(1,2)= 18. If f has a saddle point at (1,2), then one of the following statements is true Select one: a. None of the choices is correct answer bif y(1,2) is less than - 3 or greater than 3 c.f xa {1,2) is less than 3 and greater than - 3 d. fxr (1,2) is less than 6 and greater...
vector calculus.
Do
both please
Q1: What, in your own words, is the difference between a partial derivative and a directional derivative? How are they similar? Give a particular example to illustrate your explanations (choose some function z=f(x,y)) Q2: Given a surface z= f(x,y), a point (x,yo) in the domain of f, and a unit vector i pointing some direction in the xy-plane, what does it mean if D,f(x,Y)=0? Be as specific as possible.
Q1: What, in your own words,...
Question 6 10 points Save Ans Determine the partial derivative of the following function with respect to "z" and evaluate at point A:(-3,4,-2): f(x, y, z) = axºyz+b yºxz+cz*yx Uses the following values: a=4; b=3; and c=1.
What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2)? -8 -3 4 12 b) c) d) e) none of these 113 113 V13 113 a) o What is the average rate of change of z = f(x, y) = x² + xy(with respect to horizontal distance) as one travels from (2,1) to (4,-2)? 2 5 12 c) d) e) none of...
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