Answered: Let f(x,y) x2-2y² +3x. In what…

Let f(x,y) x2-2y² +3x. In what direction from (1,2) should we proceed so that the change in f in that direction would increase most rapidly?

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

See similar textbooks

Related questions

Q: Find the points on the curve y=x(x-1)(x-2) which have the same gradient use @ for 2

Q: 2. Find the derivative of the function at PO in the direction of u. f(x,y)=6x-7y, P0(-7,-2), u=4i-3j

A: We have to find derivative

Q: Find the direction at which the function f(x, y, 2) = a In(e-az) increases fastest at (-3,0, 0) O…

Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

Q: Find linearization of the function f(x) = Vx + 3 at a = 1 and use it to approximate V3.98

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) =

A: Topic = Functions

Q: Find the derivative of the function

A: Given that y = ( ax+ √(x2+y2)) -2 Method used- Chain rule- The chain rule states that the…

Q: Consider the function 8 · + 9. xy f(x, y) In which direction does the function f(x, y) increase most…

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 4, (1, 2) Vf(1, 2) =

Q: The second derivative , for the function 7y+ 13z 3a2 is O y = 9

A: Given query is to find the second derivative of the function.

Q: Find the gradient of the function at the given point f(x, y) = 5x + 4y² + 1, (1,4) Vf(1, 4) =

A: Solution of given question is written in below steps.

Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

Q: 2²y. 3. Consider the function f(, y) =

Q: Find the third derivative of ƒ (z) = ¥9z +I. f" (2) =

A: Answer is mentioned below

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 10, (2, 3) Vf(2, 3) =

Q: Find the derivatives of f(x)=(ax4+b)6 and f(x)=axe-bx+15 Assume that a and b are constants.

A: Given query is to find the derivative of the expression.

Q: Find the derivative using the definition. a. f(t) 2t+1 b. g(x) = 2x² +1

Q: Find the direction at which the function f(x, y, z) = x In(e - cz) increases fastest at (-3, C O (0,…

A: To Find: The direction at which the function fx,y,z=x ln(ey -xz) increases fastest at ( -3, 0 ,0)…

Q: Find the derivative of the function. q=V19r - r7 19 - 7,6 B)- -776 1 A)· V19r - r7 2V191 - 17 C)…

Q: In what direction does f(x) = 6xy - 8x increase most rapidly at (- 9, 0)? V f( – 9, 0) =

A: Given function f(x,y) = 6xy-8x^2.

Q: Let f(x,y)=x² - 2y² + 3x. In what direction from (2, –1) should we proceed so that the change in f…

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 3y2 + 2, (3, 5) Vf(3, 5) =

A: Given: fx,y=2x+3y2+2 ; Px,y=3,5 As we know that; The expression for the gradient vector.…

Q: Let f(x, y) = xe*Y. Find the maximum rate of change of f at the point (2, 1). хе

A: We will find the maximum rate of change.

Q: Find the direction at which the function f(x, y, z) increases fastest at (2, 0, 0) = x In(e' – xz)…

Q: Find the derivative of the function. g(u) = (8+ u²)*(1 – 5u²)8 %3D = (n), 6

A: Now we will differentiate g with respect to u . And we will derivative the function using chain…

Q: Find the linear approximation of the function y = x at point xo = 1 .3 О а. у%3D Зх - 2 О Б. у3D 3х…

Q: Find the linear approximation of the function at the given point. f(x, y) = -4x²y³ at (-9,7) O A.…

A: In this question we have to find linear approximation of the given function.

Q: Suppose that g(x, y) = xf(e"v´). Find g„, 9y and gyæ in terms of the function f and its derivatives.

Q: Find the gradient of the function f(x, y) = 3x + 5y2 + 1, at the given point (2, 1)

A: Given equation - f(x,y) = 3x+5y2+1We can write it as - y = 3x+5y2+1Gradient is given by , dydxNow…

Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

Q: Find the linearization of the function f(x): L(z)= ab a --4x-5 va a न 4x+3 at z=-1 sin (a) E

Q: When we are standing at the point (1,-3), the function f(x, y) = 3x²y+xy is increasing most rapidly…

A: We have to find the direction of rapid increase.

Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y² + 4, (3, 4) Vf(3, 4) =

Q: Find the derivative of the function. 7x u2 -4 7x 7x g(x) = 5x du u2 + 4 Hint: f(u) du = f(u) du +…

Q: Find the differential of the function. u = 3x4 + 4

A: The given function u=3x4+4

Q: Find the gradient of f(x, y) = 3xty3 + 4x°y® at (1, 2).

Q: 2. Suppose that z is a function of a and y, and F(x2 - y², xy - 2², yz - 2²) = 0. Calculate and…

A: Solution :

Q: In the function f(x, y) = ((2x + 3y)^10), we need to know the derivative in relation to the variable…

Q: ) Find the direction in which f (x, y) = x²+xyincreases most rapidly at P(1, –1).

A: 1.) given multivariable function is, fx,y=x2+xy and point is P(1,-1). Divergence: Divergence of the…

Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 7x + 8y.…

A: Directional derivative: - The partial derivatives of f give the slopes ∂f∂x in the positive…

Q: Under what conditions is a linear function f(x)=mx+b,m≠0, a linear function?

A: Here I am attaching image so that you understand each and every step.

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4)

A: To find the gradient of the function at the given point.

Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,

Q: Find the derivative of the function. g(x) = [*- 1 -dt -5 2+4 10 а. 841 b. 2x (x²+ 4)² 1 С. x²+4

Q: 4. What is the direction in which the function f(x, y) = yx² -- decreases most rapidly at the point…

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

Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-3,0, (0,…

A: Sorry I cannot recognize your given points. So I provide only methods of problem you can easily…

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4) Vf(1, 4) =

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

I need the answer as soon as possible

Let f(x,y)=x2-2y+3x. In what direction from (1,2) should we
proceed so that the change inf in that direction would increase
most rapidly?
O a. toward (5, - 8)
O b. toward (0,0)
O c. toward (-4,10)
O d. toward (4,-6)
O e. toward (6,-6)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.