Question: 9. Let f ( x , y )= x^ 4 y^ 2+ y and P =(1,2). Find the unit vector that points in the direction

9. Let f(x,y)=x^4 y^2+ y and P=(1,2). Find the unit vector that points in the direction of maximum rate of increase at P. Find the rate of change in the direction A=(2,1).

10. Let f(x,y)=x^2+xy+y^2. What is the direction in which f is increasing the most rapidly at the point (1,1) ? Find the directional derivative of f in this direction.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

6.4 - Directional Derivative & Gradient In #1-4, for the given function & point p & vector ?v (a) Find the gradient of the function (b) find the gradient at the point p (c) find the maximum rate of...

6. [-/8 Points] DETAILS SCALCET8 14.5.052. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x =...

please help in solving this economic question.......its a complete question * Exercise 5 A housewife buys 2 kilo of meat a week. Assume that the price of the meat increases 60.50 per kilo. Verify: a)...

I need help with these questions Suppose that over a certain region of space the electrical potential V is given by V(x. y. 2) = 7r - Ary + ryz. Find the rate of change of the potential at P(1. 3, 7)...

| Rockland Commun X W SPEECH FINAL.doc X Bb Take Test: MAT 201 x O MAT 20100-8( x Bb MAT 20100H Exam x 1; rain falling from a( x Bow Related Rates, A Cc x | Untitled * *Course Hero X DE MAT 20100H...

interpolation and the Lagrange polynomial 5. Polynomial Irrte rpolation. {a} Use the Lagrange interpolation process to obtain a polynomial of least degree that assumes these values. 1 I] 2 3 4 y i"...

Safari File Edit View History Bookmarks Window Help 70% . Tue 6:03 PM QE myopenmath.com ! c Disney On Ice 2022 Fall Term (1) Precalculus MAT 200 5551[46610] (LaG.. Homepage Ellucian Degree Works...

Assignment 7: Problem 3 Previous Problem Problem List Next Problem (1 point) The graph of the equation x2 + xy + y = 6 is an ellipse lying obliquely in the plane, as illustrated in the fig dy a....

Hey guys I need help with these questions, how can I solve them, these types are hard, the question numbers are in the pic 9. [-I4 Points] SPRECALC7 2.7.014. MY NOTl Find f+ g, f g, fg, and fly and...

Please answer all questions and show work for every question. Please provide a step by step explanations, circle the answers, and write neatly as possible. Thank you! *All the information is provided...

The adjusted balances at December 31, 2020, for Derlak Enterprises are shown in alphabetical order below: 2020 2019 Accounts payable $ 63,800 $ 11,000 Accumulated amortization, franchise 20,600...

An aluminum bar has the desired length when at 15oC. How much stress is required to keep it at this length if the temperature increases to 35oC?

Question 2 6 ( 2 points ) Listen The cost to a member bank of borrowing from the Federal Reserve is called the: a ) discount rate. b ) reserve requirement. C ) price of securities in the open market....

The purpose of this assignment is to use an affinity diagram to brainstorm and identify root causes of the organizational problem and potential solutions for addressing it. Now that you have...

1. Strategy refers to the general policies that managers adopt to increase A. Costs. B. The number of client meetings. C. The rate of technological change. D. The generation of profits. 2. As opposed...

Answer the following questions: 1. What aspects of HP University effectively link training to the organization's needs? 2. Which aspects of the "university" link employee development to the...

The Internet provides an unprecedented amount of information by way of blogs, videos, and podcasts. Conduct a critique of one blog, one video, and one podcast, which provide information that...

How the Internet Changed Business: Identifying the Ten Competitive Landscape Changing Properties and the 5 Cs and how they shape and affect a firms business model and thus, performance.

What is v for the H beta line? Question 9 What is v for the H gamma line? Question 10 What is v for the O II line? Now, v=cz, where v is the recessional velocity and c is the speed of light:...

6. It is what the person has previously done for the group that is the deciding factor.

3. It is the commitment you show that is the deciding factor.

4. It is the principle of equality (according to very specific criteria of equality) that is crucial.