2nd Exam

Question 1

The gradient vector is denoted by?

1st notation

Answer 1

▼ƒ = <ƒx,ƒy,ƒz>

Question 2

The gradient vector is denoted by?

2nd notation

Answer 2

▼ƒ(x,y)=

Question 3

What’s the formula for the directional derivative?

Answer 3

Duƒ(x,y,z)=▼ƒ(x,y,z) • u

Question 4

What’s the maximum rate of change formula?

Answer 4

Question 5

What is the Second Derivative Test formula?

Answer 5

Question 6

What is it if :

Answer 6

Local minimum

Question 7

What is it if:

Answer 7

Local Maximum

Question 8

What is it if:

Answer 8

NOT a local maximum or minimum

is called a SADDLE POINT

Question 9

What is it if D=0?

Answer 9

The test gives no information it could be minimum, maximum or saddle point.

Question 10

What is the determinant of D?

Answer 10

Question 11

What is the Lagrange multiplier formula to find maximum and minimum values subject to constrains?

Answer 11

Question 12

For the Lagrange multiplier how do I know which values are the maximum or minimum values?

Answer 12

I have to Evaluate ƒ at all points (x,y,z) that result and the largest of these values is the max and the smallest is the minimum value.

Question 13

What is the formula for the chain rule CASE 1?

Answer 13

Question 14

What is the formula for the chain rule Case 2 with respect to s?

Answer 14

Question 15

What is the formula for the chain rule Case 2 with respect to t?

Answer 15