**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