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