Gradient and directional derivative Quiz
10 questions · easy to harder · Calculus 3 · score and step-by-step answers
How it works
- 10 questions, about 30 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 2 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise the lesson with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
1 Question 1
Find the gradient of f(x, y) = x2 y at (1, 2).Type the answer.
2 Question 2
Find the gradient of f(x, y) = xy at (2, 3).Type the answer.
3 Question 3
Find the gradient of f(x, y) = 4x − 2y + xy at (1, 2).Type the answer.
4 Question 4
Find the gradient of f(x, y) = x3 − xy at (2, 1).Type the answer.
5 Question 5
Directional derivative of f(x, y) = x2 + y2 at (1, 2) in the direction of <3, 4>- A) D_uf = 22
- B) D_uf = 5
- C) D_uf = 225
6 Question 6
Directional derivative of f(x, y) = x2 y at (1, 3) in the direction of <0, 1>Type the answer.
7 Question 7
Directional derivative of f(x, y) = x3 + 2y2 at (1, −1) in the direction of <5, 12>- A) D_uf = 3313
- B) D_uf = −3313
- C) D_uf = −33
- D) D_uf = 13
8 Question 8
Find the gradient of f(x, y, z) = x2 + y2 + z2 at (1, 2, 2).Type the answer.
9 Question 9
Maximum rate of change of f(x, y) = xy at (3, 4)Type the answer.
10 Question 10
Maximum rate of change of f(x, y) = 3x + 4y at (1, 1)Type the answer.