Exam 4: Extension E: Applications of Differentiation

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.

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

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 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.

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

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

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

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?

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?

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

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.

What is the minimum vertical distance between the parabolas and ?