 3.7.1: Numerical, Graphical, and Analytic Analysis Find two positive numbe...
 3.7.2: Numerical, Graphical, and Analytic Analysis An open box of maximum ...
 3.7.3: In Exercises 3 8, find two positive numbers that satisfy the given ...
 3.7.4: In Exercises 3 8, find two positive numbers that satisfy the given ...
 3.7.5: In Exercises 3 8, find two positive numbers that satisfy the given ...
 3.7.6: In Exercises 3 8, find two positive numbers that satisfy the given ...
 3.7.7: In Exercises 3 8, find two positive numbers that satisfy the given ...
 3.7.8: In Exercises 3 8, find two positive numbers that satisfy the given ...
 3.7.9: In Exercises 9 and 10, find the length and width of a rectangle tha...
 3.7.10: In Exercises 9 and 10, find the length and width of a rectangle tha...
 3.7.11: In Exercises 11 and 12, find the length and width of a rectangle th...
 3.7.12: In Exercises 11 and 12, find the length and width of a rectangle th...
 3.7.13: In Exercises 1316, find the point on the graph of the function that...
 3.7.14: In Exercises 1316, find the point on the graph of the function that...
 3.7.15: In Exercises 1316, find the point on the graph of the function that...
 3.7.16: In Exercises 1316, find the point on the graph of the function that...
 3.7.17: Chemical Reaction In an autocatalytic chemical reaction, the produc...
 3.7.18: Traffic Control On a given day, the flow rate (cars per hour) on a ...
 3.7.19: Area A farmer plans to fence a rectangular pasture adjacent to a ri...
 3.7.20: Maximum Area A rancher has 200 feet of fencing with which to enclos...
 3.7.21: Maximum Volume (a) Verify that each of the rectangular solids shown...
 3.7.22: Maximum Volume Determine the dimensions of a rectangular solid (wit...
 3.7.23: Maximum Area A Norman window is constructed by adjoining a semicirc...
 3.7.24: Maximum Area A rectangle is bounded by the and axes and the graph o...
 3.7.25: Minimum Length A right triangle is formed in the first quadrant by ...
 3.7.26: Maximum Area Find the area of the largest isosceles triangle that c...
 3.7.27: Maximum Area A rectangle is bounded by the axis and the semicircle ...
 3.7.28: Area Find the dimensions of the largest rectangle that can be inscr...
 3.7.29: Area A rectangular page is to contain 30 square inches of print. Th...
 3.7.30: Area A rectangular page is to contain 36 square inches of print. Th...
 3.7.31: Numerical, Graphical, and Analytic Analysis An exercise room consis...
 3.7.32: Numerical, Graphical, and Analytic Analysis A right circular cylind...
 3.7.33: Maximum Volume A rectangular package to be sent by a postal service...
 3.7.34: Maximum Volume Rework Exercise 33 for a cylindrical package. (The c...
 3.7.35: Maximum Volume Find the volume of the largest right circular cone t...
 3.7.36: Maximum Volume Find the volume of the largest right circular cylind...
 3.7.37: The perimeter of a rectangle is 20 feet. Of all possible dimensions...
 3.7.38: The perimeter of a rectangle is 20 feet. Of all possible dimensions...
 3.7.39: Minimum Surface Area A solid is formed by adjoining two hemispheres...
 3.7.40: Minimum Cost An industrial tank of the shape described in Exercise ...
 3.7.41: Minimum Area The sum of the perimeters of an equilateral triangle a...
 3.7.42: Maximum Area Twenty feet of wire is to be used to form two figures....
 3.7.43: Beam Strength A wooden beam has a rectangular cross section of heig...
 3.7.44: Minimum Length Two factories are located at the coordinates and wit...
 3.7.45: Projectile Range The range of a projectile fired with an initial ve...
 3.7.46: Conjecture Consider the functions and on the domain (a) Use a graph...
 3.7.47: Illumination A light source is located over the center of a circula...
 3.7.48: Illumination The illumination from a light source is directly propo...
 3.7.49: Minimum Time A man is in a boat 2 miles from the nearest point on t...
 3.7.50: Minimum Time Consider Exercise 49 if the point is on the shoreline ...
 3.7.51: Minimum Time The conditions are the same as in Exercise 49 except t...
 3.7.52: Minimum Time When light waves, traveling in a transparent medium, s...
 3.7.53: Sketch the graph of on the interval (a) Find the distance from the ...
 3.7.54: Minimum Cost An offshore oil well is 2 kilometers off the coast. Th...
 3.7.55: Minimum Force A component is designed to slide a block of steel wit...
 3.7.56: Maximum Volume A sector with central angle is cut from a circle of ...
 3.7.57: Numerical, Graphical, and Analytic Analysis The cross sections of a...
 3.7.58: Maximum Profit Assume that the amount of money deposited in a bank ...
 3.7.59: Minimum Cost The ordering and transportation cost of the components...
 3.7.60: Diminishing Returns The profit (in thousands of dollars) for a comp...
 3.7.61: Minimum Distance In Exercises 6163, consider a fuel distribution ce...
 3.7.62: Minimum Distance In Exercises 6163, consider a fuel distribution ce...
 3.7.63: Minimum Distance In Exercises 6163, consider a fuel distribution ce...
 3.7.64: Maximum Area Consider a symmetric cross inscribed in a circle of ra...
 3.7.65: Find the maximum value of on the set of all real numbers satisfying...
 3.7.66: Find the minimum value of for 22y
Solutions for Chapter 3.7: Optimization Problems
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 3.7: Optimization Problems
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus, edition: 8. Calculus was written by and is associated to the ISBN: 9780618502981. This expansive textbook survival guide covers the following chapters and their solutions. Since 66 problems in chapter 3.7: Optimization Problems have been answered, more than 84236 students have viewed full stepbystep solutions from this chapter. Chapter 3.7: Optimization Problems includes 66 full stepbystep solutions.

Divisor of a polynomial
See Division algorithm for polynomials.

Equal matrices
Matrices that have the same order and equal corresponding elements.

Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).

Horizontal line
y = b.

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Inverse variation
See Power function.

Multiplication principle of counting
A principle used to find the number of ways an event can occur.

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Pointslope form (of a line)
y  y1 = m1x  x 12.

Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Real number
Any number that can be written as a decimal.

Regression model
An equation found by regression and which can be used to predict unknown values.

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Summation notation
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

Velocity
A vector that specifies the motion of an object in terms of its speed and direction.

Vertex of an angle
See Angle.

Zero matrix
A matrix consisting entirely of zeros.