 13.8.1: In Exercises 16, identify any extrema of the function by recognizin...
 13.8.2: In Exercises 16, identify any extrema of the function by recognizin...
 13.8.3: In Exercises 16, identify any extrema of the function by recognizin...
 13.8.4: In Exercises 16, identify any extrema of the function by recognizin...
 13.8.5: In Exercises 16, identify any extrema of the function by recognizin...
 13.8.6: In Exercises 16, identify any extrema of the function by recognizin...
 13.8.7: In Exercises 716, examine the function for relative extrema.fx, y 3...
 13.8.8: In Exercises 716, examine the function for relative extrema.
 13.8.9: In Exercises 716, examine the function for relative extrema.fx, y x...
 13.8.10: In Exercises 716, examine the function for relative extrema.fx, y 2...
 13.8.11: In Exercises 716, examine the function for relative extrema.z x2 xy...
 13.8.12: In Exercises 716, examine the function for relative extrema.
 13.8.13: In Exercises 716, examine the function for relative extrema.fx, y x...
 13.8.14: In Exercises 716, examine the function for relative extrema.hx, y x...
 13.8.15: In Exercises 716, examine the function for relative extrema.gx, y 4...
 13.8.16: In Exercises 716, examine the function for relative extrema.fx, y x...
 13.8.17: In Exercises 1720, use a computer algebra system to graph the surfa...
 13.8.18: In Exercises 1720, use a computer algebra system to graph the surfa...
 13.8.19: In Exercises 1720, use a computer algebra system to graph the surfa...
 13.8.20: In Exercises 1720, use a computer algebra system to graph the surfa...
 13.8.21: In Exercises 2128, examine the function for relative extrema and sa...
 13.8.22: In Exercises 2128, examine the function for relative extrema and sa...
 13.8.23: In Exercises 2128, examine the function for relative extrema and sa...
 13.8.24: In Exercises 2128, examine the function for relative extrema and sa...
 13.8.25: In Exercises 2128, examine the function for relative extrema and sa...
 13.8.26: In Exercises 2128, examine the function for relative extrema and sa...
 13.8.27: In Exercises 2128, examine the function for relative extrema and sa...
 13.8.28: In Exercises 2128, examine the function for relative extrema and sa...
 13.8.29: In Exercises 29 and 30, examine the function for extrema without us...
 13.8.30: In Exercises 29 and 30, examine the function for extrema without us...
 13.8.31: Think About It In Exercises 3134, determine whether there is a rela...
 13.8.32: Think About It In Exercises 3134, determine whether there is a rela...
 13.8.33: Think About It In Exercises 3134, determine whether there is a rela...
 13.8.34: Think About It In Exercises 3134, determine whether there is a rela...
 13.8.35: A function has continuous second partial derivatives on an open reg...
 13.8.36: A function has continuous second partial derivatives on an open reg...
 13.8.37: In Exercises 37 42, (a) find the critical points, (b) test for rela...
 13.8.38: In Exercises 37 42, (a) find the critical points, (b) test for rela...
 13.8.39: In Exercises 37 42, (a) find the critical points, (b) test for rela...
 13.8.40: In Exercises 37 42, (a) find the critical points, (b) test for rela...
 13.8.41: In Exercises 37 42, (a) find the critical points, (b) test for rela...
 13.8.42: In Exercises 37 42, (a) find the critical points, (b) test for rela...
 13.8.43: In Exercises 43 and 44, find the critical points of the function an...
 13.8.44: In Exercises 43 and 44, find the critical points of the function an...
 13.8.45: In Exercises 4554, find the absolute extrema of the function over t...
 13.8.46: In Exercises 4554, find the absolute extrema of the function over t...
 13.8.47: In Exercises 4554, find the absolute extrema of the function over t...
 13.8.48: In Exercises 4554, find the absolute extrema of the function over t...
 13.8.49: In Exercises 4554, find the absolute extrema of the function over t...
 13.8.50: In Exercises 4554, find the absolute extrema of the function over t...
 13.8.51: In Exercises 4554, find the absolute extrema of the function over t...
 13.8.52: In Exercises 4554, find the absolute extrema of the function over t...
 13.8.53: In Exercises 4554, find the absolute extrema of the function over t...
 13.8.54: In Exercises 4554, find the absolute extrema of the function over t...
 13.8.55: The figure shows the level curves for an unknown function What, if ...
 13.8.56: The figure shows the level curves for an unknown function What, if ...
 13.8.57: In Exercises 5759, sketch the graph of an arbitrary function satisf...
 13.8.58: In Exercises 5759, sketch the graph of an arbitrary function satisf...
 13.8.59: In Exercises 5759, sketch the graph of an arbitrary function satisf...
 13.8.60: Consider the functions and (a) Show that both functions have a crit...
 13.8.61: True or False? In Exercises 6164, determine whether the statement i...
 13.8.62: True or False? In Exercises 6164, determine whether the statement i...
 13.8.63: True or False? In Exercises 6164, determine whether the statement i...
 13.8.64: True or False? In Exercises 6164, determine whether the statement i...
Solutions for Chapter 13.8: Extrema of Functions of Two Variables
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 13.8: Extrema of Functions of Two Variables
Get Full SolutionsCalculus was written by and is associated to the ISBN: 9780547167022. This textbook survival guide was created for the textbook: Calculus , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Since 64 problems in chapter 13.8: Extrema of Functions of Two Variables have been answered, more than 61157 students have viewed full stepbystep solutions from this chapter. Chapter 13.8: Extrema of Functions of Two Variables includes 64 full stepbystep solutions.

Arcsine function
See Inverse sine function.

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Continuous function
A function that is continuous on its entire domain

Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian threedimensional space

Degree
Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution

Differentiable at x = a
ƒ'(a) exists

Equilibrium point
A point where the supply curve and demand curve intersect. The corresponding price is the equilibrium price.

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

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Hypotenuse
Side opposite the right angle in a right triangle.

Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.

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

Limit
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

Local extremum
A local maximum or a local minimum

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Real number line
A horizontal line that represents the set of real numbers.

Sample space
Set of all possible outcomes of an experiment.

System
A set of equations or inequalities.

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Xscl
The scale of the tick marks on the xaxis in a viewing window.