

Understanding Gradients
Interactive Video
•
Mathematics, Science
•
10th - 12th Grade
•
Practice Problem
•
Hard
Aiden Montgomery
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the function used to introduce the concept of gradients?
f(x, y) = x^2 + y^2
f(x, y) = x^2 + xy + y^2
f(x, y) = x^2 - xy + y^2
f(x, y) = x^2 + 2xy + y^2
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the gradient operator in two-dimensional space consist of?
Partial derivatives with respect to x and y
Partial derivatives with respect to x, y, and z
Partial derivatives with respect to x and z
Partial derivatives with respect to y and z
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the gradient of a function represented?
As a scalar value
As a matrix
As a complex number
As a vector
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the partial derivative of the function f(x, y) = x^2 + xy + y^2 with respect to x?
2x + y
2y + x
x + y
2x + 2y
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In which direction does the gradient vector point?
In the direction of the minimum slope
In the direction of the maximum slope
In the direction of zero slope
In the direction of the average slope
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the gradient tell you about the slope in the x-y plane?
The direction of no slope
The direction of the average slope
The direction of the maximum slope
The direction of the minimum slope
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens when you add the vectors of partial derivatives in the x and y directions?
You get a matrix
You get a complex number
You get the gradient vector
You get a scalar value
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