Deck 4: Extension E: Applications of Differentiation

Question 1

What is the minimum vertical distance between the parabolas and ?

Answer 1

31/8

Question 2

A steel pipe is being carried down a hallway 14 ft wide.At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide.What is the length of the longest pipe that can be carried horizontally around the corner?

Answer 2

27.50 ft

Question 3

Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L = 8 and width W = 3.

Answer 3

60.5

Question 4

The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares?

Question 5

A farmer with 710 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.What is the largest possible total area of the four pens?

Question 6

Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L = 9 cm if one side of the rectangle lies on the base of the triangle. Round your answer to the nearest tenth.

A) 5.5 cm, 4.4 cm
B) 4 cm, 3.91 cm
C) 4.5 cm, 4 cm
D) 4.5 cm, 3.9 cm
E) 7.5 cm, 2.9 cm
F) 9.5 cm, 3.9 cm

Question 7

A woman at a point A on the shore of a circular lake with radius wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time.She can walk at the rate of and row a boat at How should she proceed? (Find ).Round the result,if necessary,to the nearest hundredth.

A) radians
B) She should row from point A to point C radians
C) radians
D) radians
E) She should walk around the lake from point A to point C.

Question 8

Find two positive numbers whose product is and whose sum is a minimum.

A)
B) 3, 48
C)
D) 6, 24
E) 2, 72

Question 9

Find an equation of the line through the point (8,16) that cuts off the least area from the first quadrant.

Question 10

A rectangular storage container with an open top is to have a volume of 10 The length of its base is twice the width.Material for the base costs $12 per square meter.Material for the sides costs $5 per square meter.Find the cost of materials for the cheapest such container.

A) $158.1
B) $153.92
C) $152.4
D) $153.9
E) $152.9
F) $151.6

Question 11

Find the point on the line that is closest to the origin.

A)
B)
C)
D)
E)

Question 12

A piece of wire 10 m long is cut into two pieces.One piece is bent into a square and the other is bent into an equilateral triangle.How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.

A) 4.35 m
B) 3.25 m
C) 0 m
D) 5.35 m
E) 4.4 m