Consider v 3u Is the directional derivative of a differentiable function f (x, y) in the direction of v at the point (x 0 , y 0 ) three times the directional derivative of f in the direction of u at the point (x 0 , y 0 ) Explain

Question: Consider v = 3u. Is the directional derivative of a differentiable function f (x, y) in the direction of v at the point (x 0

Consider v = 3u. Is the directional derivative of a differentiable function f (x, y) in the direction of v at the point (x₀, y₀) three times the directional derivative of f in the direction of u at the point (x₀, y₀)? Explain.

Step by Step Solution

★★★★★

3.45 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

No the directional derivative of a differentiable function fx y in the direction of v at the po... 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!

Blue Computers, a major server manufacturer in the U.S. currently has plants in Kentucky and Pennsylvania. The Kentucky plant has a capacity of 1 million units a year and the Pennsylvania plant has a...

Determine Elite Health's (an HMO) per-member-per-month capitation cost amount if the expected encounters per year = 5 and the cost per encounter = $80. 2) Would primary care physicians in at Elite...

Let f: X Y be differentiable at x0 with derivative Df[x0], and let x be a vector of unit norm (||x|| = 1). Show that the directional derivative of f at x0 in the direction x is the value of the...

Use Theorem 13.9 to find the directional derivative of the function at P in the direction of v. (x, y) = xy, P(-5 5), v = 3i - 4j Data from in Theorem 13.9 THEOREM 13.9 Directional Derivative If f is...

Calculus 3 Section 14.5 Reading Assignment: Directional Derivatives and Gradient Vectors I am suck with this question. Please help! Section 14.5 Reading Assignment: Directional Derivatives and...

MA 261 PRACTICE PROBLEMS 1. If the line ` has symmetric equations y x1 z+2 2 = 3 = 7 , nd a vector equation for the line `0 that contains the point (2; 1; 3) and is parallel to `. A. ~ = (1 + 2t)~...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

854 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES 9. 20. Jessica and I at 2 oh ; h (x , y ) = -, x = 1/2, y = 1712 paths that make a with velocity va 10. "J : f ( x , y , Z ) = xy - 22, x = rcos0,...

The questions are in the photos below: I would like them all solved correctly. Question 5 True or false: This piecewise function is differentiable at x = -1. Not yet answered f (x ) = 3x +6 ifx 5-1...

For each point (x, y, z) on a surface S, let n(x, y, z) be a unit normal vector to S at (x, y, z). The so called normal derivative of a differentiable function f: R R is the directional derivative...

Determine the directional derivative of the given function in the indicated direction and at the indicated point. f (x, y) = x cos(y), in the direction of = , at (1, /4)

The influence of IS managers Board-level representation for IS managers is essential in the e-business era.

Sunshine Company began operations on January 1, 2020. In its first year, the following transactions occurred: 1. Issued common shares for $330,000 cash. 2. Borrowed $59,000 from the bank for a...

Term Answer Description Rebate A . The purchase of a good or service without fully considering your priorities and the availability of any alternatives.Impulse purchase B . The popular name given to...

=+(like a math SAT). In such situations one cannot spend too much time on any one problem. When you take such a test, how do you decide when to give up on a problem and move on to the next problem?...

Find div(F x G) = . (F x G). F(x, y, z)=xi - zk G(x, y, z) = xi+yj + zk

Define the divergence of a vector field in the plane and in space.

Find the area of the lateral surface (see figure) over the curve C in the xy-plane and under the surface z = (x, y), where Lateral surface area (x, y) = x - y + 4, C: x + y = 4 = [50 C f(x, y) ds.

accounting help please:) Use the following information for the Exercises below. (Algo) [The following information applies to the questions displayed below] NewTech purchases computer equipment for...

b. All periods preceding the date that a bargain purchase option becomes exercisable All periods representing renewals or extensions of the lease term at the lessor's option a. All periods beyond the...

Company A manufactures and selts one product for $14 per unit Required: a) Determine the profit equation. b) Use the equation to calculate profit if the volume is 6,200 units