Question

In what direction does ?(?,?)= ln(9?^2+6?^2) increase most rapidly at (2,5)? (Enter a unit vector.)

In what direction does ?(?,?)= ln(9?^2+6?^2) increase most rapidly at (2,5)?

(Enter a unit vector.)

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

In this question first we find directional derivative and then find the direction in which function increases rapidly. Hope you understand the solution.

Thank you

Please like

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In what direction does f(x,y)=ln(7x^2+8y^2) increase most rapidly at (4,5)? Answer with a unit vector
In what direction does f(x,y)=ln(7x^2+8y^2) increase most rapidly at (4,5)? Answer with a unit vector
Find the directions in which the function increases and decreases most rapidly at Upper P 0....
Find the directions in which the function increases and decreases most rapidly at Upper P 0. Then find the derivatives of the function in those directions. f(x,y,z)=3ln(xy)+ln (yz)+2ln(xz) P0(1,1,1) 1. In which direction does the function increase most​ rapidly? u=____i+_____j+____k 2. In which direction does the function decrease most​ rapidly? -u=____i+____j+____k 3. What is the value of the derivative in the direction of u? 4. What is the value of the derivative in the direction of minus−u​?
Let f(x, y) = x^2 ln(x^3 + y). (a) Find the gradient of f. (b) Find...
Let f(x, y) = x^2 ln(x^3 + y). (a) Find the gradient of f. (b) Find the direction in which the function decreases most rapidly at the point P(2, 1). (Give the direction as a unit vector.) (c) Find the directions of zero change of f at the point P(2, 1). (Give both directions as a unit vector.)
Find the unit vector of direction of the following vector F → = ( 3.0 i...
Find the unit vector of direction of the following vector F → = ( 3.0 i ^ − 2.0 j ^ ) Enter the x-component and y-component of the unit vector, rounding to 2 decimal places.
What is the length of the projection of the unit vector of the direction unit vector...
What is the length of the projection of the unit vector of the direction unit vector of the line x = 1 + 2t, y = 3-t, z = 5 + 2t overthe vector of the plane 2x + 3y-6z + 8 = 0? If your answer is a fraction write it in the abcd / efgh style (no spaces between what you write)
(a) Show that a differentiable function f decreases most rapidly at x in the direction opposite...
(a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the gradient vector, that is, in the direction of −∇f(x). Let θ be the angle between ∇f(x) and unit vector u. Then Du f = |∇f| Correct: Your answer is correct. . Since the minimum value of Correct: Your answer is correct. is -1 Correct: Your answer is correct. occurring, for 0 ≤ θ < 2π, when θ = Correct: Your answer is correct....
What is the projection of the unit vector of the direction of the line x= 1...
What is the projection of the unit vector of the direction of the line x= 1 + 2t, y= 3-t, z= 5 + 2t on the normal vector of the plane 2x+3y-6z+8=0? If your answer is a fraction write it in the abcd/efgh style.
6. (5 marks) Consider the function f defined by f (x, y) = ln(x − y)....
6. Consider the function f defined by f (x, y) = ln(x − y). (a) Determine the natural domain of f. (b) Sketch the level curves of f for the values k = −2, 0, 2. (c) Find the gradient of f at the point (2,1), that is ∇f(2,1). (d) In which unit vector direction, at the point (2,1), is the directional derivative of f the smallest and what is the directional derivative in that direction?
In general, using diagrams / examples to generalize: what direction does the acceleration vector point in...
In general, using diagrams / examples to generalize: what direction does the acceleration vector point in 2D & 3D motion? (there is not a specific example, just give an example of a 2D & 3D situation and what direction the acceleration vector points in those examples).
] Consider the function f : R 2 → R defined by f(x, y) = x...
] Consider the function f : R 2 → R defined by f(x, y) = x ln(x + 2y). (a) Find the gradient of f(x, y) at the point P(e/3, e/3). (b) Use the gradient to find the directional derivative of f at P(e/3, e/3) in the direction of the vector ~u = h−4, 3i. (c) Find a unit vector (based at P) pointing in the direction in which f increases most rapidly at P.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT