 4.3.1: The sum of two nonnegative numbers is 100. What is the maximum valu...
 4.3.2: The product of two positive numbers is 784. What is the minimum val...
 4.3.3: The sum of three nonnegative numbers is 36, and one of the numbers ...
 4.3.4: The perimeter of a rectangle is 64 cm. Find the lengths of the side...
 4.3.5: If you have 100 feet of fencing and want to enclose a rectangular a...
 4.3.6: A closed rectangular box, with a square base x by x cm and height h...
 4.3.7: An opentopped rectangular box, with a square base x by x cm and he...
 4.3.8: A closed cylinder with radius r cm and height h cm.
 4.3.9: A closed cylinder with radius r cm and height h cm.
 4.3.10: In Exercises 1011, find the xvalue maximizing the shaded area. One...
 4.3.11: In Exercises 1011, find the xvalue maximizing the shaded area. One...
 4.3.12: A rectangle has one side on the xaxis and two vertices on the curv...
 4.3.13: A right triangle has one vertex at the origin and one vertex on the...
 4.3.14: A rectangle has one side on the xaxis, one side on the yaxis, one...
 4.3.15: Find analytically the exact critical point of the function which re...
 4.3.16: Of all rectangles with given area, A, which has the shortest diagonals
 4.3.17: A rectangular beam is cut from a cylindrical log of radius 30 cm. T...
 4.3.18: In 1819 a vertical line divides a region into two pieces. Find the ...
 4.3.19: In 1819 a vertical line divides a region into two pieces. Find the ...
 4.3.20: In 2022 the figures are made of rectangles and semicircles. (a) Fin...
 4.3.21: In 2022 the figures are made of rectangles and semicircles. (a) Fin...
 4.3.22: In 2022 the figures are made of rectangles and semicircles. (a) Fin...
 4.3.23: A piece of wire of length L cm is cut into two pieces. One piece, o...
 4.3.24: In 2427, find the minimum and maximum values of the expression wher...
 4.3.25: In 2427, find the minimum and maximum values of the expression wher...
 4.3.26: In 2427, find the minimum and maximum values of the expression wher...
 4.3.27: In 2427, find the minimum and maximum values of the expression wher...
 4.3.28: Which point on the curve y = 1 x is closest to the origin?
 4.3.29: Find the point(s) on the ellipse x2 9 + y2 = 1 (a) Closest to the p...
 4.3.30: What are the dimensions of the closed cylindrical can that has surf...
 4.3.31: A hemisphere of radius 1 sits on a horizontal plane. A cylinder sta...
 4.3.32: In a chemical reaction, substance A combines with substance B to fo...
 4.3.33: A smokestack deposits soot on the ground with a concentration inver...
 4.3.34: A wave of wavelength traveling in deep water has speed, v, given fo...
 4.3.35: A circular ring of wire of radius r0 lies in a plane perpendicular ...
 4.3.36: a mass of m kg. If her arm makes an angle of with her body (assumed...
 4.3.37: Four equally massive particles can be made to rotate, equally space...
 4.3.38: Four equally massive particles can be made to rotate, equally space...
 4.3.39: Four equally massive particles can be made to rotate, equally space...
 4.3.40: A business sells an item at a constant rate of r units per month. I...
 4.3.41: A bird such as a starling feeds worms to its young. To collect worm...
 4.3.42: On the same side of a straight river are two towns, and the townspe...
 4.3.43: A pigeon is released from a boat (point B in Figure 4.44) floating ...
 4.3.44: To get the best view of the Statue of Liberty in Figure 4.45, you s...
 4.3.45: A light ray starts at the origin and is reflected off a mirror alon...
 4.3.46: (a) For which positive number x is x1/x largest? Justify your answe...
 4.3.47: The arithmetic mean of two numbers a and b is defined as (a+b)/2; t...
 4.3.48: A line goes through the origin and a point on the curve y = x2e3x, ...
 4.3.49: The distance, s, traveled by a cyclist, who starts at 1 pm, is give...
 4.3.50: When birds lay eggs, they do so in clutches of several at a time. W...
 4.3.51: Let f(v) be the amount of energy consumed by a flying bird, measure...
 4.3.52: The forward motion of an aircraft in level flight is reduced by two...
 4.3.53: Let f(v) be the fuel consumption, in gallons per hour, of a certain...
 4.3.54: If A is the area of a rectangle of sides x and 2x, for 0 x 10, the ...
 4.3.55: An open box is made from a 20inch square piece of cardboard by cut...
 4.3.56: The solution of an optimization problem modeled by a quadratic func...
 4.3.57: The solution of an optimization problem modeled by a quadratic func...
 4.3.58: A context for a modeling problem where you are given that xy = 120 ...
 4.3.59: A modeling problem where you are minimizing the cost of the materia...
 4.3.63: If a differentiable function f(x) has a global maximum on the inter...
Solutions for Chapter 4.3: OPTIMIZATION AND MODELING
Full solutions for Calculus: Single Variable  6th Edition
ISBN: 9780470888643
Solutions for Chapter 4.3: OPTIMIZATION AND MODELING
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643. Since 60 problems in chapter 4.3: OPTIMIZATION AND MODELING have been answered, more than 33368 students have viewed full stepbystep solutions from this chapter. Chapter 4.3: OPTIMIZATION AND MODELING includes 60 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Conditional probability
The probability of an event A given that an event B has already occurred

Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)

Deductive reasoning
The process of utilizing general information to prove a specific hypothesis

Dependent event
An event whose probability depends on another event already occurring

Direct variation
See Power function.

Double inequality
A statement that describes a bounded interval, such as 3 ? x < 5

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

Frequency table (in statistics)
A table showing frequencies.

Jump discontinuity at x a
limx:a  ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

Limaçon
A graph of a polar equation r = a b sin u or r = a b cos u with a > 0 b > 0

Logistic regression
A procedure for fitting a logistic curve to a set of data

Minor axis
The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Ordered set
A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

Positive angle
Angle generated by a counterclockwise rotation.

Positive numbers
Real numbers shown to the right of the origin on a number line.

Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.

Subtraction
a  b = a + (b)

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

yintercept
A point that lies on both the graph and the yaxis.