Gradient and directional derivative Quiz

Name: ______________________   Date: __________   Score: ____ / 10

10 questions. Calculator allowed. Show your working. steplyclass.com/calculus-3/gradient-and-directional-derivative/quiz/

1. 1

   Find the gradient of f(x, y) = x² y at (1, 2).

   Answer: ____________________

2. 2

   Find the gradient of f(x, y) = xy at (2, 3).

   Answer: ____________________

3. 3

   Find the gradient of f(x, y) = 4x − 2y + xy at (1, 2).

   Answer: ____________________

4. 4

   Find the gradient of f(x, y) = x³ − xy at (2, 1).

   Answer: ____________________

5. 5

   Directional derivative of f(x, y) = x² + y² at (1, 2) in the direction of <3, 4>
   1. A) D_uf = 22
   2. B) D_uf = 5
   3. C) D_uf = 225

6. 6

   Directional derivative of f(x, y) = x² y at (1, 3) in the direction of <0, 1>

   Answer: ____________________

7. 7

   Directional derivative of f(x, y) = x³ + 2y² at (1, −1) in the direction of <5, 12>
   1. A) D_uf = 3313
   2. B) D_uf = −3313
   3. C) D_uf = −33
   4. D) D_uf = 13

8. 8

   Find the gradient of f(x, y, z) = x² + y² + z² at (1, 2, 2).

   Answer: ____________________

9. 9

   Maximum rate of change of f(x, y) = xy at (3, 4)

   Answer: ____________________

10. 10

    Maximum rate of change of f(x, y) = 3x + 4y at (1, 1)

    Answer: ____________________