Each side of a cardboard square is 12 inches, What is the maximum volume of a box that can be made from the square by cutting congruent squares from the corners and turning up the four sides ?
Title: Oct 19­4:33 PM (1 of 25)
Title: Oct 20­3:49 PM (2 of 25)
2. A 25 ft long, rectangular sheet of metal, 12 inches wide, is to be made into a rain gutter by turning up two sides s that they are perpendicular to the sheet. How many inches should be turned up to give the gutter its greatest capacity?
Title: Oct 19­4:36 PM (3 of 25)
4. A rectangle has its base on the x axis and its upper corners on the parabola y = 6 ­ x2. Find the maximum possible area of the rectangle.
Title: Oct 19­4:38 PM (4 of 25)
5. A rectangle is inscribed between the graphs of y = 4 ­ x2 and
y = (1/4)x4 ­ 1. Find the width of the rectangle that has the largest area.
Title: Oct 19­4:39 PM (5 of 25)
Title: Oct 20­3:52 PM (6 of 25)
6. Find the maximum distance , measured vertically, between the
graphs of y = x and y = x1/3 Title: Oct 19­4:41 PM (7 of 25)
Title: Oct 20­3:58 PM (8 of 25)
7. A cardboard box of 108 cm 3 volume with a square base and no top is to be constructed. Find the minimum area of the cardboard needed. Title: Oct 19­2:48 PM (9 of 25)
The minimum area of cardboard needed is 108 cm2.
Title: Oct 19­2:53 PM (10 of 25)
8. Mr. Phillips decides to have a completely feced in rectangular garden. It will be laid out so that one side is adjacent to his neighbor's property. The neighbor agrees to pay for half of that part of the fence which will border his property. The graden is to contain 432 square yards. What dimensions should Mr. Phillips select for his garden so that his own cost will be a minimum?
Title: Oct 19­4:42 PM (11 of 25)
Title: Oct 20­4:05 PM (12 of 25)
9. A rectangle is inscribed in a right triangle with side 6, 8, and 10. Two sides of the rectangle lie along legs of the triangle, and the remaining vertex of the rectangle is on the hypotenuse of the triangle. What dimensions for the rectangle will maximize its area ?
Title: Oct 19­4:42 PM (13 of 25)
Title: Oct 20­4:10 PM (14 of 25)
10. What is the x coordinate of the point on the curve y = ex that is closest to the origin ? Give your answer accurate to the nearest hundredth.
Title: Oct 19­4:48 PM (15 of 25)
Title: Oct 20­4:16 PM (16 of 25)
11. A rectangle is inscribed under one "bump" of the cosine curve, with two vertices on the x axis and the other two vertices on the curve y = cos(x) where
a) What is the area of the rectangle, given in terms of the x coordinate of one of the vertices on the x axis ?
b) What is the maximum possible area of the triangle ?
Title: Oct 19­4:50 PM (17 of 25)
13. A boater finds herself 4 miles from the nearest point to a straight shoreline which is 6 miles from a shoreside motel. She plans to row ashore and then walk to the motel. If she can walk at 3 mph, at what speed must she be able to row so that the quickest way to get to the motel is to row directly ?
Title: Oct 23­7:32 AM (18 of 25)
Title: Oct 23­10:27 AM (19 of 25)
14. A rectangle is drawn with sides parallel to the coordinate axes and with its upper two vertices on the parabola and its lower two vertices on the parabola What is the maximum possible area of the rectangle ?
Title: Oct 23­7:35 AM (20 of 25)
15. Let A(x) be the area of the rectangle inscribed under the curve
with vertices at (x,0 ) and (­x,0), where a) Determine A(1).
b) Determine the greates possible value for A(x).
Title: Oct 23­7:38 AM (21 of 25)
Title: Oct 23­10:37 AM (22 of 25)
16.A particle moves along the x axis so that at any time t, its position is given by Detemine the particle's maximum velocity.
Title: Oct 23­7:43 AM (23 of 25)
17. Estimate the shortest distance from the point (5,3) to the nearest point on the graph of Title: Oct 23­7:45 AM (24 of 25)
18. A company is designing shipping crates and wants the volume of each crate to be a square between 1 and 1.5 feet per side. The material for the bottom costs $5, the sides $3 and the top $1 per square foot. What dimensions will give the minimum cost ?
Title: Oct 23­7:47 AM (25 of 25)