 4.1: If f is a function of classC2 and p2 denotes the secondorder Taylor...
 4.2: The increment f of a function f (x, y) measures the change in the z...
 4.3: The differential d f of a function f (x, y) measures the change in ...
 4.4: The secondorder Taylor polynomial of f (x, y,z) = x 2 + 3x z + y2 ...
 4.5: The secondorder Taylor polynomial of f (x, y) = x 3 + 2x y + y at ...
 4.6: The secondorder Taylor polynomial of f (x, y) = x 3 + 2x y + y at ...
 4.7: Near the point (1, 3, 5), the function f (x, y,z) = 3x 4 + 2y3 + z2...
 4.8: The Hessian matrix H f (x1,..., xn) of f has the property that H f ...
 4.9: If f (a1,..., an) = 0, then f has a local extremum at a = (a1,..., ...
 4.10: If f is differentiable and has a local extremum at a = (a1,..., an)...
 4.11: The set {(x, y,z)  4 x 2 + y2 + z2 9} is compact
 4.12: The set {(x, y)  2x 3y = 1} is compact.
 4.13: Any continuous function f (x, y) must attain a global maximum on th...
 4.14: Any continuous function f (x, y,z) must attain a global maximum on ...
 4.15: If f (x, y) is of class C2, has a critical point at (a, b), and fx ...
 4.16: If det H f (a) = 0, then f has a saddle point at a.
 4.17: The function f (x, y,z) = x 3 y2z x 2(y + z) has a saddle point at ...
 4.18: The function f (x, y,z) = x 2 + y2 + z2 yz has a local maximum at (...
 4.19: The function f (x, y,z) = x y3 x 2z + z has a degenerate critical p...
 4.20: The function F(x1,..., xn) = 2(x1 1)2 3(x2 2)2 ++ (1)n+1(n + 1)(xn ...
 4.21: The function F(x1,..., xn) = 2(x1 1)2 3(x2 2)2 ++ (1)n+1(n + 1)(xn ...
 4.22: All local extrema of a function of more than one variable occur whe...
 4.23: All points a = (a1,..., a2) where the function f (x1,..., xn) has a...
 4.24: Any solution (1,...,k , x1,..., xn) to the system of equations f x1...
 4.25: To find the critical points of the function f (x, y,z, w) subject t...
 4.26: Suppose that f (x, y,z) and g(x, y,z) are of class C1 and that (x0,...
 4.27: The critical points of f (x, y,z) = x y + 2x z + 2yz subject to the...
 4.28: Given data points (3, 1), (4, 10), (5, 8), (6, 12), to find the bes...
 4.29: All equilibrium points of a gradient vector field are minimum point...
 4.30: Given an output function for a company, the marginal change in outp...
Solutions for Chapter 4: Maxima and Minima in Several Variables
Full solutions for Vector Calculus  4th Edition
ISBN: 9780321780652
Solutions for Chapter 4: Maxima and Minima in Several Variables
Get Full SolutionsChapter 4: Maxima and Minima in Several Variables includes 30 full stepbystep solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Since 30 problems in chapter 4: Maxima and Minima in Several Variables have been answered, more than 12867 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Acute triangle
A triangle in which all angles measure less than 90°

Additive inverse of a real number
The opposite of b , or b

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Frequency distribution
See Frequency table.

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

Identity properties
a + 0 = a, a ? 1 = a

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Leading term
See Polynomial function in x.

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)

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

Quotient rule of logarithms
logb a R S b = logb R  logb S, R > 0, S > 0

Rational zeros
Zeros of a function that are rational numbers.

Residual
The difference y1  (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

Riemann sum
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

Sequence of partial sums
The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Time plot
A line graph in which time is measured on the horizontal axis.

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.