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Worksheet: Directional Derivatives
Q1:
The temperature of a solid is given by the function , where , , are space coordinates relative to the center of the solid. In which direction from the point will the temperature decrease the fastest?
- A decreases the fastest in the direction of .
- B decreases the fastest in the direction of .
- C decreases the fastest in the direction of .
- D decreases the fastest in the direction of .
Q2:
Find the directional derivative of at the point in the direction of .
- A
- B
- C
- D
- E
Q3:
Compute the gradient of .
- A
- B
- C
- D
- E
Q4:
Find the directional derivative of at the point in the direction of .
- A
- B
- C
- D
- E
Q5:
Find the directional derivative of at the point in the direction of .
- A
- B
- C
- D
- E
Q6:
Find the directional derivative of at the point in the direction of .
- A
- B
- C
- D
- E
Q7:
Find the directional derivative of at the point in the direction of .
- A
- B
- C
- D
- E4
Q8:
In which direction does the function increases the fastest from the point ? In which direction does it decrease the fastest? Give your answer using unit vectors.
- A increases the fastest in the direction of and decreases the fastest in the direction of .
- B increases the fastest in the direction of and decreases the fastest in the direction of .
- C increases the fastest in the direction of and decreases the fastest in the direction of .
- D increases the fastest in the direction of and decreases the fastest in the direction of .
Q9:
Find the directional derivative of at the point in the direction of .
- A
- B
- C
- D
- E