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Math
Calculus
Calculus, Early Transcendentals
Chapter 4.7, Problem 1AP
Chapter 4.7, Problem 1AP
BUY
Calculus, Early Transcendentals
9th Edition
ISBN:
9781337613927
Author: Stewart
Publisher:
CENGAGE L
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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4.1 Maximum And Minimum Values
4.2 The Mean Value Theorem
4.3 What Derivatives Tell Us About The Shape Of A Graph
4.4 Indeterminate Forms And L'hospital's Rule
4.5 Summary Of Curve Sketching
4.6 Graphing With Calculus And Technology
4.7 Optimization Problems
4.8 Newton's Method
4.9 Antiderivatives
Chapter Questions
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Problem 1E: Consider the following problem: Find two numbers whose sum is 23 and whose product is a maximum. (a)...
Problem 2E: Find two numbers whose difference is 100 and whose product is a minimum.
Problem 3E: Find two positive numbers whose product is 100 and whose sum is a minimum.
Problem 4E: The sum of two positive numbers is 16. What is the smallest possible value of the sum of their...
Problem 5E: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for 1 x ...
Problem 6E: What is the minimum vertical distance between the parabolas y = x2 + 1 and y = x x2?
Problem 7E: Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible.
Problem 8E: Find the dimensions of a rectangle with area 1000 m2 whose perimeter is as small as possible.
Problem 9E: A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the...
Problem 10E: The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is...
Problem 11E: Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area...
Problem 12E: Consider the following problem: A box with an open top is to be constructed from a square piece of...
Problem 13E: A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide...
Problem 14E: A farmer has 1200ft of fencing for enclosing a trapezoidal field along a river as shown. One of the...
Problem 15E: A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his bam. No...
Problem 16E: If the farmer in Exercise 15 wants to enclose 8000 square feet of land, what dimensions will...
Problem 17E: (a) Show that of all the rectangles with a given area, the one with smallest perimeter is a square....
Problem 18E: A box with a square base and open top must have a volume of 32,000cm3 . Find the dimensions of the...
Problem 19E: If 1200 cm2 of material is available to make a box with a square base and an open top, find the...
Problem 20E: A box with an open top is to be constructed from a 4ft by 3ft rectangular piece of cardboard by...
Problem 21E: A rectangular storage container with an open top is to have a volume of 10 m3. The length of its...
Problem 22E: Rework Exercise 21 assuming the container has a lid that is made from the same material as the...
Problem 23E: A package to be mailed using the US postal service may not measure more than 108 inches in length...
Problem 24E: Refer to Exercise 23. Find the dimensions of the cylindrical mailing tube of greatest volume that...
Problem 25E: Find the point on the line y = 2x + 3 that is closest to the origin.
Problem 26E: Find the point on the curve y=x that is closest to the point (3, 0).
Problem 27E: Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0).
Problem 28E: Find, correct to two decimal places, the coordinates of the point on the curve y = sin x that is...
Problem 29E: Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r.
Problem 30E: Find the area of the largest rectangle that can be inscribed in the ellipse x2/a2 + y2/b2 = 1.
Problem 31E: Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral...
Problem 32E: Find the area of the largest trapezoid that can be inscribed in a circle of radius 1 and whose base...
Problem 33E: Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of...
Problem 34E: If the two equal sides of an isosceles triangle have length a, find the length of the third side...
Problem 35E: If one side of a triangle has length a and another has length 2a , show that the largest possible...
Problem 36E
Problem 37E: A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of...
Problem 38E: A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest...
Problem 39E: A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible surface...
Problem 40E: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the...
Problem 41E: The top and bottom margins of a poster are each 6cm and the side margins are each 4cm . If the area...
Problem 42E: A poster is to have an area of 180 in2 with 1-inch margins at the bottom and sides and a 2-inch...
Problem 43E: A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is...
Problem 44E
Problem 45E: If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice...
Problem 46E
Problem 47E: A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a...
Problem 48E: A cone-shaped paper drinking cup is to be made to hold 27 cm3 of water. Find the height and radius...
Problem 49E: A cone with height h is inscribed in a larger cone with height H so that its vertex is at the center...
Problem 50E: An object with weight W is dragged along a horizontal plane by a force acting along a rope attached...
Problem 51E: If a resistor of R ohms is connected across a battery of E volts with internal resistance r ohms,...
Problem 52E: For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is...
Problem 53E: In a beehive, each cell is a regular hexagonal prism, open at one end with a trihedral angle at the...
Problem 54E: A boat leaves a dock at 2:00 pm and travels due south at a speed of 20 km/h. Another boat has been...
Problem 55E: EXAMPLE 4 A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants...
Problem 56E: A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C...
Problem 57E: An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to...
Problem 58E
Problem 59E: The illumination of an object by a light source is directly proportional to the strength of the...
Problem 60E: Find an equation of the line through the point (3, 5) that cuts off the least area from the first...
Problem 61E
Problem 62E
Problem 63E: What is the shortest possible length of the line segment that is cut off by the first quadrant and...
Problem 64E: What is the smallest possible area of the triangle that is cut off by the first quadrant and whose...
Problem 65E
Problem 66E: (a) Show that if the profit P(x) is a maximum, then the marginal revenue equals the marginal cost....
Problem 67E: A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at 10, the...
Problem 68E: During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the...
Problem 69E: A retailer has been selling 1200 tablet computers a week at 350 each. The marketing department...
Problem 70E: A company operates 16 oil wells in a designated area. Each pump, on average, extracts 240 barrels of...
Problem 71E: Show that of all the isosceles triangles with a given perimeter, the one with the greatest area is...
Problem 72E
Problem 73E: Consider the tangent line to the ellipse x2a2+y2b2=1 at a point (p, q) in the first quadrant. (a)...
Problem 74E: The frame for a kite is to be made from six pieces of wood. The four exterior pieces have been cut...
Problem 75E: A point P needs to be located somewhere on the line AD so that the total length L of cables linking...
Problem 76E: The graph shows the fuel consumption c of a car (measured in gallons per hour) as a function of the...
Problem 77E: Let v1 be the velocity of light in air and v2 the velocity of light in water. According to Fermats...
Problem 78E: Two vertical poles PQ and ST are secured by a rope PRS going from the top of the first pole to a...
Problem 79E: The upper right-hand corner of a piece of paper, 12 in. by 8 in., as in the figure, is folded over...
Problem 80E: A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a...
Problem 81E: An observer stands at a point P, one unit away from a track. Two runners start at the point S in the...
Problem 82E: A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the...
Problem 83E: Where should the point P be chosen on the line segment AB so as to maximize the angle ?
Problem 84E: A painting in an art gallery has height h and is hung so that its lower edge is a distance d above...
Problem 85E
Problem 86E: The blood vascular system consists of blood vessels (arteries, arterioles, capillaries, and veins)...
Problem 87E: Ornithologists have determined that some species of birds tend to avoid flights over large bodies of...
Problem 88E: Two light sources of identical strength are placed 10 m apart. An object is to be placed at a point...
Problem 1AP
Problem 2AP
Problem 3AP
Problem 4AP
Problem 5AP
Problem 1.1AP
Problem 1.2AP
Problem 1.3AP
Problem 1.4AP
Problem 1.5AP
Problem 1.6AP
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