Answered: Find the unit vector u along which the…

Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the point (2,1) is maximum. What is this maximum rate of change?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 27E

See similar textbooks

Related questions

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

Q: Find the directional derivative of f(x, y, z) = zy + xª at the point (2, 1, 3) in the direction of a…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y): 4x sin(xy)…

Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

Q: Let f(x, y) = x²y'. At the point (-1, 2), find a vector (a) In the direction of maximum rate of…

Q: In what direction ữ is f(x, y, z) increasing most rapidly at the point (1, 1, 0)? Give your answer…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(zy)…

A: The maximum rate of change of a function f(x, y) at (a, b) occurs in the direction ∇f(a, b) where…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(xy)…

Q: Let f (x, y) = x 4y-2 and P = (2, 1). Find the unit vector that points in the direction of maximum…

A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

Q: Find the increase rate of the scalar V at point P from origin to the point P(2,6; 9,8 ; 9,5) where…

A: According to question given that The origin to the point P(2,6 ;9,8 ; 9,5) where V=3, 3xy+ 2, 6xyz

Q: Find a vector equation of the tangent line of f(t) = (cost, sint, t) at the point Po (0, 1,

Q: Determine the rate of change at (0, 2) of the function 1 h (x, y) V1+x² + 2y² in the direction of…

Q: Q1. Calculate the directional derivative of f (x, y, z) of vector v =i+2j+3k. = xyz at point P =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the directional derivative of the function f(x,y, z) = V22+ y² + z² at point (2, -3, 6) in the…

A: In this question, we want to find the directional derivative of the given function at given point…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, y)…

A: Given: fx,y=4yx at point 4,5 The rate of change of f is ∇fx,y=∂f∂x,∂f∂y…

Q: Again just working on examples for exam, would like to see how you solve this to see if it is the…

Q: Find the directional derivative of the function z(x, y) = In(x² + y²) at the point M(xo, Yo), in the…

A: The directional derivative of function z=fx,y in the direction vector u is calculated by the formula…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) : 5x sin(xy)…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

Q: Let f(x, y, z) = 3ex cos(yz). a) Find the directional derivative of f at P(0, 0, 0) in the…

A: Given , fx,y,z=3ex cos4zwe have to find directional derivative of f at p 0,0,0 in the directionof…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

Q: Find the direction in which the maximum rate of change occurs for the function f(z,9)2zsin(ay) at…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

A: Given: fx,y,z=3x+7yz 1,7,-1 To find: Maximum rate of change of f at the given point. The…

Q: Find the maxcimum rate of change of f at the given point and the direction in which it occurs. F(x,…

Q: Find a unit vector in the direction in which f (x, y, z) = 3x³z² + 3y°z + 24z – 4 increases most…

Q: 3. Find the directional derivative of f(x, y, z) =x*y-yz' +z at the point (1, -2,0) in the direction…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The objective is to find the maximum rate of change of f at the given point and the direction in…

Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: According to the given information, it is required to find the maximum rate of change of f at the…

Q: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

Q: Find the maximum rate of change of f(x, y) Maximum rate of change: = In(x² + y?) at the point (3, 1)…

Q: Find the maximum rate of change of f(x, y) = In(x² + y?) at the point (-4, -3) and the direction in…

A: Given: f(x,y)=ln(x2+y2) at point (-4,-3) to find: maximum rate of change

Q: Find the directional derivative of the function f(x, y, z) = /ryz at the point P(2,2, 2) in the…

A: Topic-vector calculas

Q: Consider the function defined by 1 g(x, y) = cos (Tx Vy) + log3 (x – y) Calculate the instantaneous…

Q: a) What is the rate of change of f(x, y) = 3xy + y^2 at the point (2, 4) in the direction of vector…

A: (a) Given Data: Function: f(x, y)=3xy+y2 Point: (x, y)=(2, 4) Direction of vector: v=-3i-j The…

Q: What is the rate of change of the function f(x,y) = ye^(2cos x) + tan(x+3y) at ( 3π/2 , π/2) in the…

A: Given: fx,y=ye2cosx+tanx+3y To Find: Rate of change of fx,y in the direction of the vector 3,4 at…

Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 5x + 6y at the point…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: 2. Calculate the instantaneous rate of change of g at the point (4, 1,0) in the direction of the…

A: Please see the attachment

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: The given function isfx, y=5x.sin(xy)to find the direction in which the maximum rate of change…

Q: Choose the direction vector for which the function f defined by f(x, y)= sin(5x) cos(3y) has the…

Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

Q: Find the a unit vector in the direction of which f(x, y) = In (1 + xy) increases the most rapidly at…

A: Consider the given function as fx,y=ln1+xy

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: We have to find the direction in which the maximum rate of change occurs for the function…

Q: Find the directional derivative of f(x,y)=sin(2x−2y) at the point (π/2,π/6)in the direction of the…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

Q: Let f(x, y) = x /G. At the point (1, 4), find a vector (a) In the direction of maximum rate of…

Question

Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the point (2,1) is maximum. What is this maximum rate of change?

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution