Question: 4 Consider the function f(x,y) = x* -xy+ 3y +7 and the point P(- 1,1). a. Find the unit vectors that give the direction

4 Consider the function f(x,y) = x* -xy+ 3y +7 and the

4 Consider the function f(x,y) = x* -xy+ 3y +7 and the point P(- 1,1). a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find a vector that points in a direction of no change in the function at P.

Step by Step Solution

★★★★★

3.38 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Solution a We known that the direction of the gradient f tells us direction of the greatest incre... View full answer

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!

Consider the function f (x) = 3(x + 1)2 - 4. a. Find f (5). b. Find f (n). c. Find f (x + 2). d. Use your calculator to graph y = f (x) and y = f (x + 2) on the same axes. How do the graphs compare?

Consider the function f (x) = x2 + 4x 3. Find the average rate of change of the function from x1 to x2. (a) x1 = 1, x2 = 2 (b) x1 = 1, x2 = 1.5 (c) x1 = 1, x2 = 1.25 (d) x1 = 1, x2 = 1.125 (e) x1 =...

Consider the function f (x) = (ax) / (x b)2. (a) Determine the effect on the graph of f when b 0 and a is varied. Consider cases in which a is positive and a is negative. (b) Determine the effect...

Compute the directional derivative of the following function at the given point P in the direction of th given vector. Be sure to use a unit vector for the direction vector. f ( x, y ) = In (4 +x2 +...

Please Answer the following questions (SHOW ALL WORK PLEASE) 1. Consider the function Hag-Ir} = e \"[2 I5 _ 5'2 I5 and the point P1: 3, 3}. 3. Find the unit vectors that give the direction of...

(3) Consider the function f(x, y) = 4 - ply + y2 + 6 and the point P(-1, 1). (a) Find the unit vector that gives the direction of steepest ascent at P. (b) Find the unit vector that gives the...

It might be appreciated that you help me to figure out answers and steps too.. I don't know where to start with.. so please give me detailed steps. Question 1 (22 marks) 6 -2 - Given that a 3x3 real...

Consider the following functions and points P.a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P.b. Find a vector that points in a direction of no change in...

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

Please help! Clear Handwriting 1. 1. (3.5pts - show work, use g = 9.8m/s' and round your final answer to two decimal places as needed) A projectile is launched from the ground (thus, the initial...

Hyper gravity at its Ames Research Center, NASA uses its large ''2().G" centrifuge to test the effects of very large accelerations (''hyper gravity'') on test pilots and astronauts. In this device,...

What are gains from trade? What is the primary benefit of trade? Why is the idea that trade is beneficial counter-intuitive? Discuss.

Which of the following statements about Porter s diamond of national advantage is NOT true? Question 3 5 options: Demanding consumers drive firms in the country to meet high standards, upgrade...

The following data refer to Twisto Pretzel Company for the year 20x 1. Work-In-process inventory, 12/31/x0 .............................................$ 8,100 Selling and administrative salaries...

An electric field of 260 000 N/C points due west at a certain spot. What are the magnitude and direction of the force that acts on a charge of -7.0 C at this spot?

A small spherical insulator of mass 8.00 10-2 kg and charge +0.600 C is hung by a thread of negligible mass. A charge of -0.900 C is held 0.150 m away from the sphere and directly to the right of...

The drawing shows an equilateral triangle, each side of which has a length of 2.00 cm. Point charges are fixed to each corner, as shown. The 4.00 C charge experiences a net force due to the charges...

A charge +q is located at the origin, while an identical charge is located on the x axis at x = +0.50 m. A third charge of +2q is located on the x axis at such a place that the net electrostatic...

Dan, the owner of Dan's Diner, decided to change the brand of hot dogs served in his establishment. Dan advertised widely that he now served only Doggie Dogs. Dan made the change on the basis of the...

4 Consider the function f (x) = x 2+x a) Create the Power Series for f(x) and determine the interval of convergence. b) Let g(x) = Jf(x)dx . Use your answer from part (a) and write the first 5 terms...

Hi, below are the photos of the question plz answer all questions and there is no need to give the explanation for the answer just fill the right blanks thanks Also, make sure the answers are right...

Consider the function f ( x) = tan -1( tan x ). Then f (0) =f (x) =0. Your professor claims that by the Mean Value Theorem, there is a number con (0, x) such that f(c) =0. (a) Prove your professor...

Econ 289 Assignment 2 (Sections 4.1-4.5) Questions Solve all questions, showing your work in reasonable detail. Finish your calculations: when the results can be reduced to numbers, calculate those...

2. (10 pts) Consider the function f (x) = v9-x. (a) (3 pts) Sketch the the curves f (x), x =5, and y = 0. Shade the region enclosed by these curves. 3 (b) (3 pts) Using n = 4 subintervals, sketch the...

Please show work Given the function . - F ( x ) = x 3 - 3 x+5 calculate the average rate of change over the interval ( - 1, 4) 2) Given h ( x ) = ( 2 x - 5 ) 2 Find two functions f ( x ) and olx )...