Question 1
Which of the following is a use of the gradient vector?
Question 2
How is the maximum value of the directional derivative determined?
Question 3
What role does the cosine function play in the relationship between the directional derivative and the gradient vector?
Question 4
What happens to the directional derivative when the direction vector u is perpendicular to the gradient vector?
Question 5
What is a directional derivative?
Question 6
How is the gradient of a function f denoted and computed?
Question 7
What is the directional derivative of f(x, y) = x/y at the point (6, -2) in the direction of the vector V(-1, 3)?
Question 8
Which formula represents the directional derivative of a function f at point (x0, y0) in the direction of a unit vector u with components (a, b)?
Question 9
How is the tangent plane to a surface f(x, y, z) = k computed using the gradient?
Question 10
In which direction does the gradient vector point?
Question 11
What is the condition for the directional derivative to be the minimum value?
Question 12
How do you convert a given vector V to a unit vector for use in calculating directional derivatives?
Question 13
What is the relationship between the gradient vector and a tangent plane to a surface?
Question 14
What do partial derivatives with respect to X or Y represent in a function of two variables?
Question 15
Which principle explains why the gradient vector is used to find the maximum rate of increase?