 12.9.1: Explain why, at a point that maximizes or minimizes f subject to a ...
 12.9.2: If f 1x, y2 = x2 + y2 and g1x, y2 = 2x + 3y  4 = 0, write the Lagr...
 12.9.3: If f 1x, y, z2 = x2 + y2 + z2 and g1x, y, z2 = 2x + 3y  5z + 4 = 0...
 12.9.4: Sketch several level curves of f 1x, y2 = x2 + y2 and sketch the co...
 12.9.5: 514. Lagrange multipliers in two variables Use Lagrange multipliers...
 12.9.6: 514. Lagrange multipliers in two variables Use Lagrange multipliers...
 12.9.7: 514. Lagrange multipliers in two variables Use Lagrange multipliers...
 12.9.8: 514. Lagrange multipliers in two variables Use Lagrange multipliers...
 12.9.9: 514. Lagrange multipliers in two variables Use Lagrange multipliers...
 12.9.10: 514. Lagrange multipliers in two variables Use Lagrange multipliers...
 12.9.11: 514. Lagrange multipliers in two variables Use Lagrange multipliers...
 12.9.12: 514. Lagrange multipliers in two variables Use Lagrange multipliers...
 12.9.13: 514. Lagrange multipliers in two variables Use Lagrange multipliers...
 12.9.14: 514. Lagrange multipliers in two variables Use Lagrange multipliers...
 12.9.15: 1524. Lagrange multipliers in three variables Use Lagrange multipli...
 12.9.16: 1524. Lagrange multipliers in three variables Use Lagrange multipli...
 12.9.17: 1524. Lagrange multipliers in three variables Use Lagrange multipli...
 12.9.18: 1524. Lagrange multipliers in three variables Use Lagrange multipli...
 12.9.19: 1524. Lagrange multipliers in three variables Use Lagrange multipli...
 12.9.20: 1524. Lagrange multipliers in three variables Use Lagrange multipli...
 12.9.21: 1524. Lagrange multipliers in three variables Use Lagrange multipli...
 12.9.22: 1524. Lagrange multipliers in three variables Use Lagrange multipli...
 12.9.23: 1524. Lagrange multipliers in three variables Use Lagrange multipli...
 12.9.24: 1524. Lagrange multipliers in three variables Use Lagrange multipli...
 12.9.25: 2534. Applications of Lagrange multipliers Use Lagrange multipliers...
 12.9.26: 2534. Applications of Lagrange multipliers Use Lagrange multipliers...
 12.9.27: 2534. Applications of Lagrange multipliers Use Lagrange multipliers...
 12.9.28: 2534. Applications of Lagrange multipliers Use Lagrange multipliers...
 12.9.29: 2534. Applications of Lagrange multipliers Use Lagrange multipliers...
 12.9.30: 2534. Applications of Lagrange multipliers Use Lagrange multipliers...
 12.9.31: 2534. Applications of Lagrange multipliers Use Lagrange multipliers...
 12.9.32: 2534. Applications of Lagrange multipliers Use Lagrange multipliers...
 12.9.33: 2534. Applications of Lagrange multipliers Use Lagrange multipliers...
 12.9.34: 2534. Applications of Lagrange multipliers Use Lagrange multipliers...
 12.9.35: 3538. Maximizing utility functions Find the values of / and g with ...
 12.9.36: 3538. Maximizing utility functions Find the values of / and g with ...
 12.9.37: 3538. Maximizing utility functions Find the values of / and g with ...
 12.9.38: 3538. Maximizing utility functions Find the values of / and g with ...
 12.9.39: Explain why or why not Determine whether the following statements a...
 12.9.40: 4045. Alternative method Solve the following problems from Section ...
 12.9.41: 4045. Alternative method Solve the following problems from Section ...
 12.9.42: 4045. Alternative method Solve the following problems from Section ...
 12.9.43: 4045. Alternative method Solve the following problems from Section ...
 12.9.44: 4045. Alternative method Solve the following problems from Section ...
 12.9.45: 4045. Alternative method Solve the following problems from Section ...
 12.9.46: 4649. Absolute maximum and minimum values Find the absolute maximum...
 12.9.47: 4649. Absolute maximum and minimum values Find the absolute maximum...
 12.9.48: 4649. Absolute maximum and minimum values Find the absolute maximum...
 12.9.49: 4649. Absolute maximum and minimum values Find the absolute maximum...
 12.9.50: 5051. Graphical Lagrange multipliers The following figures show the...
 12.9.51: 5051. Graphical Lagrange multipliers The following figures show the...
 12.9.52: Extreme points on flattened spheres The equation x2n + y2n + z2n = ...
 12.9.53: 5355. Production functions Economists model the output of manufactu...
 12.9.54: 5355. Production functions Economists model the output of manufactu...
 12.9.55: Given the production function P = f 1K, L2 = KaL1  a and the budge...
 12.9.56: Temperature of an elliptical plate The temperature of points on an ...
 12.9.57: Find the maximum value of x1 + x2 + x3 + x4 subject to the conditio...
 12.9.58: Generalize Exercise 57 and find the maximum value of x1 + x2 + g+ x...
 12.9.59: Generalize Exercise 57 and find the maximum value of a1x1 + a2 x2 +...
 12.9.60: Geometric and arithmetic means Given positive numbers x1, c, xn, pr...
 12.9.61: with two constraints Given a differentiable function w = f 1x, y, z...
 12.9.62: The planes x + 2z = 12 and x + y = 6 intersect in a line L. Find th...
 12.9.63: Find the maximum and minimum values of f 1x, y, z2 = xyz subject to...
 12.9.64: The paraboloid z = x2 + 2y2 + 1 and the plane x  y + 2z = 4 inters...
 12.9.65: Find the maximum and minimum values of f 1x, y, z2 = x2 + y2 + z2 o...
Solutions for Chapter 12.9: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 12.9
Get Full SolutionsSince 65 problems in chapter 12.9 have been answered, more than 54570 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. Chapter 12.9 includes 65 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This expansive textbook survival guide covers the following chapters and their solutions.

Arcsine function
See Inverse sine function.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

Elements of a matrix
See Matrix element.

Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.

Frequency
Reciprocal of the period of a sinusoid.

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Horizontal line
y = b.

Horizontal Line Test
A test for determining whether the inverse of a relation is a function.

Imaginary part of a complex number
See Complex number.

Multiplicative identity for matrices
See Identity matrix

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

nth root of a complex number z
A complex number v such that vn = z

Order of magnitude (of n)
log n.

Positive association
A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

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.

Root of an equation
A solution.

RRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the righthand end point of each subinterval.

Slopeintercept form (of a line)
y = mx + b

Solution set of an inequality
The set of all solutions of an inequality