Deck 11: Extension G: Partial Derivatives

Question 1

Find and classify the relative extrema and saddle points of the function for and

A) Relative maximum
B) Saddle point
C) Relative minimum
D) None

Answer 1

None

Question 2

Suppose (1,1)is a critical point of a function f with continuous second derivatives. In the case of , , what can you say about f ?

A) f has a saddle point at (1,1)
B) f has a local minimum at (1,1)
C) f has a local maximum at (1,1)

Answer 2

f has a local minimum at (1,1)

Question 3

Find the critical points of the function.

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the points on the surface that are closest to the origin.

A)
B)
C)
D)
E)

Question 5

Find the absolute extrema of the function on the closed triangular region with vertices , and

A) Absolute minimum 5, Absolute maximum 17
B) Absolute minimum 0, Absolute maximum 5
C) Absolute minimum -5, Absolute maximum 5
D) Absolute minimum -5, Absolute maximum 17

Question 6

Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is

A) , ,
B) 4, 8, 16
C) 32, , 16
D) , ,
E) 32, 32, 32

Question 7

Find the local maximum,and minimum value and saddle points of the function.

Question 8

Find the absolute minimum value of the function on the set D.D is the region bounded by the parabola and the line

A) 0
B)
C)
D)
E) 30

Question 9

A cardboard box without a lid is to have a volume of cm Find the dimensions that minimize the amount of cardboard used.

Question 10

Find three positive numbers whose sum is and whose product is a maximum.

Question 11

Find three positive numbers whose sum is and whose product is a maximum.

A)
B)
C)
D)
E)

Question 12

Find the shortest distance from the point to the plane

A)
B)
C)
D)
E)

Question 13

Find the dimensions of the rectangular box with largest volume if the total surface area is given as

A) 21 cm, 14 cm, 1.75 cm
B) 14cm, 1.75 cm, 1.75 cm
C) 7 cm, 7 cm, 7cm
D) 294 cm, 7 cm, 7cm
E) 14 cm, 14 cm, 3.5 cm

Question 14

Find and classify the relative extrema and saddle points of the function