Question: What is the derivative of a function (x, y) at a point P 0 in the direction of a unit vector u? What rate does

What is the derivative of a function ƒ(x, y) at a point P₀ in the direction of a unit vector u? What rate does it describe? What geometric interpretation does it have? Give examples.

Step by Step Solution

★★★★★

3.50 Rating (150 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The derivative of a function x y at a point P0 in the direction of a unit vector u is known as the d... 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 Precalculus Questions!

How is the derivative of a differentiable function (x, y, z) at a point P 0 in the direction of a unit vector u related to the scalar component of () P 0 in the direction of u? Give reasons for your...

A formula for the derivative of a function is given. How many critical numbers does have? f'(x) = 5e-0.1|x| sin x - 1

A film studio in Hollywood produces movies according to the function (yes, they can also produce fractions of movies... Think of half a movie as a B-movie or so.) q = F(K, L) = K0.5L 0.5 /100.(reads...

Compute the directional derivative of the following function at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector. 2 3 f(x,y) = 19 -x" - 3y...

Rasmussen College - MH210 - Week 9 Assignment Problem 1 1. Plot the function below. (, )=sin cos Type your answer here. Rasmussen College - MH210 - Week 9 Assignment Problem 2 2. Find the limit...

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...

A,b,c,d please Consider the function f(x,y,z) = 2 + 2xyz, the point P(1,1, - 1), and the unit vector u = a. Compute the gradient of f and evaluate it at P. b. Find the unit vector in the direction of...

Fx(a, b, c)(x 15.5 EXERCISES Preliminary Questions 1. Which of the following is a possible value of the gradient Vf of a 4. function f(x. y) of two variables? po W (a) 5 (b) (3,4) (c) (3, 4. 5) 2....

solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks. 1. [-11 Points] DETAILS SCALCETQ 14.6.004.EP. Consider the following. x,...

(1) Consider the following system of linear equations 3x + 2y + 203 = -13 -5 5x + 2ay - 3: = -18 where a E R is a constant. (a) Classify the system according to the values of a b) Solve the above...

Gold Clothiers reported the following selected items at September 30, 2016 (last years2015amounts also given as needed): Accounts Payable .......... $ 331,000 Cash ................. 302,900...

The Rango Inc. at December 31 has cash $30,000, noncash assets $90,000, liabilities $45,000, and the following capital balances: Bruce $50,000 and Lee $25,000. The firm is liquidated, and $115,000 in...

on October 1 5 , Eric accepted a $ 5 , 0 0 0 , 6 0 - day, 8 % note from Nisha Granting a time extension on a past - due amount. Eric discounted the note at valve bank at 9 % on October 2 6 . use...

test hypotheses about the distribution of a categorical variable using a goodness-of-fit test and interpret the results in context.

Consider two ellipses, where the foci of the first ellipse are farther apart than the foci of the second ellipse. Is the eccentricity of the first ellipse always greater than the eccentricity of the...

Find a polar equation for the conic with its focus at the pole and the given vertex or vertices. Conic Ellipse Vertex (2.0), or Vertices (8, 7)

Find a polar equation for the conic with its focus at the pole and the given vertex or vertices. Conic Parabola Vertex or Vertices (5, )

What skills are needed by accountants to address the standards for both GAAP and IFRS? How can accountants acquire these skills?

Assume Nortel Networks contracted to provide a customer with Internet infrastructure for $2,000,000. The project began in 2013 and was completed in 2014. Data relating to the contract are summarized...

Why does a company debit Purchases instead of Inventory