Directional Derivatives
1. What is the primary purpose of directional derivatives?
a) To measure the area under a curve
b) To measure the rate of change of a function in a specific direction
c) To find the maximum value of a function
d) To calculate the limit of a function
2. Which of the following is a requirement for the direction vector used in
directional derivatives?
a) It must be a non-zero vector
b) It must be a unit vector
c) It can be any vector
d) It must be a two-dimensional vector
3. What does the directional derivative Duf(a, b) represent?
a) The average rate of change of the function
b) The instantaneous rate of change of the function at a point in the direction
of u
c) The total change in the function over an interval
d) The second derivative of the function
4. For a ternary function w = f(x, y, z), how is the directional derivative defined?
a) Duf(x₀, y₀, z₀) is the limit of the function as h approaches infinity
b) Duf(x₀, y₀, z₀) is the limit of the function as h approaches 0
1. What is the primary purpose of directional derivatives?
a) To measure the area under a curve
b) To measure the rate of change of a function in a specific direction
c) To find the maximum value of a function
d) To calculate the limit of a function
2. Which of the following is a requirement for the direction vector used in
directional derivatives?
a) It must be a non-zero vector
b) It must be a unit vector
c) It can be any vector
d) It must be a two-dimensional vector
3. What does the directional derivative Duf(a, b) represent?
a) The average rate of change of the function
b) The instantaneous rate of change of the function at a point in the direction
of u
c) The total change in the function over an interval
d) The second derivative of the function
4. For a ternary function w = f(x, y, z), how is the directional derivative defined?
a) Duf(x₀, y₀, z₀) is the limit of the function as h approaches infinity
b) Duf(x₀, y₀, z₀) is the limit of the function as h approaches 0
