 4.6.1: Consider the following problem: Find two numbers whose sum is 23 an...
 4.6.2: Find two numbers whose difference is 100 and whose product is a min...
 4.6.3: Find two positive numbers whose product is 100 and whose sum is a m...
 4.6.4: The sum of two positive numbers is 16. What is the smallest possibl...
 4.6.5: Find the dimensions of a rectangle with perimeter 100 m whose area ...
 4.6.6: Find the dimensions of a rectangle with area whose perimeter is as ...
 4.6.7: A model used for the yield of an agricultural crop as a function of...
 4.6.8: The rate at which photosynthesis takes place for a species of phyto...
 4.6.9: Consider the following problem: A farmer with 750 ft of fencing wan...
 4.6.10: Consider the following problem: A box with an open top is to be con...
 4.6.11: If 1200 cm of material is available to make a box with a square bas...
 4.6.12: A box with a square base and open top must have a volume of 32,000 ...
 4.6.13: (a) Show that of all the rectangles with a given area, the one with...
 4.6.14: A rectangular storage container with an open top is to have a volum...
 4.6.15: Find the points on the ellipse that are farthest away from the poin...
 4.6.16: Find, correct to two decimal places, the coordinates of the point o...
 4.6.17: Find the dimensions of the rectangle of largest area that can be in...
 4.6.18: Find the dimensions of the rectangle of largest area that has its b...
 4.6.19: A right circular cylinder is inscribed in a sphere of radius . Find...
 4.6.20: Find the area of the largest rectangle that can be inscribed in the...
 4.6.21: Find the dimensions of the isosceles triangle of largest area that ...
 4.6.22: A cylindrical can without a top is made to contain of liquid. Find ...
 4.6.23: A Norman window has the shape of a rectangle surmounted by a semici...
 4.6.24: A right circular cylinder is inscribed in a cone with height and ba...
 4.6.25: A piece of wire 10 m long is cut into two pieces. One piece is bent...
 4.6.26: A fence 8 ft tall runs parallel to a tall building at a distance of...
 4.6.27: A coneshaped drinking cup is made from a circular piece of paper o...
 4.6.28: A coneshaped paper drinking cup is to be made to hold of water. Fi...
 4.6.29: A cone with height is inscribed in a larger cone with height so tha...
 4.6.30: The graph shows the fuel consumption of a car (measured in gallons ...
 4.6.31: If a resistor of ohms is connected across a battery of volts with i...
 4.6.32: For a sh swimming at a speed relative to the water, the energy expe...
 4.6.33: In a beehive, each cell is a regular hexagonal prism, open at one e...
 4.6.34: A boat leaves a dock at 2:00 PM and travels due south at a speed of...
 4.6.35: An oil renery is located on the north bank of a straight river that...
 4.6.36: Suppose the renery in Exercise 35 is located 1 km north of the rive...
 4.6.37: The illumination of an object by a light source is directly proport...
 4.6.38: A woman at a point on the shore of a circular lake with radius 2 mi...
 4.6.39: Find an equation of the line through the point that cuts off the le...
 4.6.40: At which points on the curve does the tangent line have the largest...
 4.6.41: What is the shortest possible length of the line segment that is cu...
 4.6.42: What is the smallest possible area of the triangle that is cut off ...
 4.6.43: (a) If is the cost of producing units of a commodity, then the aver...
 4.6.44: (a) Show that if the prot is a maximum, then the marginal revenue e...
 4.6.45: A baseball team plays in a stadium that holds 55,000 spectators. Wi...
 4.6.46: During the summer months Terry makes and sells necklaces on the bea...
 4.6.47: A manufacturer has been selling 1000 television sets a week at each...
 4.6.48: The manager of a 100unit apartment complex knows from experience t...
 4.6.49: Let and be positive numbers. Find the length of the shortest line s...
 4.6.50: The frame for a kite is to be made from six pieces of wood. The fou...
 4.6.51: Let be the velocity of light in air and the velocity of light in wa...
 4.6.52: Two vertical poles and are secured by a rope going from the top of ...
 4.6.53: The upper righthand corner of a piece of paper, 12 in. by 8 in., a...
 4.6.54: A steel pipe is being carried down a hallway 9 ft wide. At the end ...
 4.6.55: Find the maximum area of a rectangle that can be circumscribed abou...
 4.6.56: A rain gutter is to be constructed from a metal sheet of width 30 c...
 4.6.57: Where should the point be chosen on the line segment so as to maxim...
 4.6.58: A painting in an art gallery has height and is hung so that its low...
 4.6.59: Ornithologists have determined that some species of birds tend to a...
 4.6.60: The blood vascular system consists of blood vessels (arteries, arte...
 4.6.61: The speeds of sound in an upper layer and in a lower layer of rock ...
 4.6.62: Two light sources of identical strength are placed 10 m apart. An o...
Solutions for Chapter 4.6: OPTIMIZATION PROBLEMS
Full solutions for Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series)  4th Edition
ISBN: 9780495559726
Solutions for Chapter 4.6: OPTIMIZATION PROBLEMS
Get Full SolutionsSingle Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) was written by Patricia and is associated to the ISBN: 9780495559726. Chapter 4.6: OPTIMIZATION PROBLEMS includes 62 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series), edition: 4. Since 62 problems in chapter 4.6: OPTIMIZATION PROBLEMS have been answered, more than 5410 students have viewed full stepbystep solutions from this chapter.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Angular speed
Speed of rotation, typically measured in radians or revolutions per unit time

Backtoback stemplot
A stemplot with leaves on either side used to compare two distributions.

Demand curve
p = g(x), where x represents demand and p represents price

Determinant
A number that is associated with a square matrix

Difference of functions
(ƒ  g)(x) = ƒ(x)  g(x)

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Expanded form
The right side of u(v + w) = uv + uw.

Future value of an annuity
The net amount of money returned from an annuity.

Graph of an inequality in x and y
The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.

Horizontal translation
A shift of a graph to the left or right.

Negative angle
Angle generated by clockwise rotation.

Polar form of a complex number
See Trigonometric form of a complex number.

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Rational expression
An expression that can be written as a ratio of two polynomials.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.
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