 4.2.1: Concerning the function f (x, y) = 4x + 6y 12 x 2 y2: (a) There is ...
 4.2.2: This problem concerns the function g(x, y) = x 2 2y2 + 2x + 3. (a) ...
 4.2.3: In Exercises 320, identify and determine the nature of the critical...
 4.2.4: In Exercises 320, identify and determine the nature of the critical...
 4.2.5: In Exercises 320, identify and determine the nature of the critical...
 4.2.6: In Exercises 320, identify and determine the nature of the critical...
 4.2.7: In Exercises 320, identify and determine the nature of the critical...
 4.2.8: In Exercises 320, identify and determine the nature of the critical...
 4.2.9: In Exercises 320, identify and determine the nature of the critical...
 4.2.10: In Exercises 320, identify and determine the nature of the critical...
 4.2.11: In Exercises 320, identify and determine the nature of the critical...
 4.2.12: In Exercises 320, identify and determine the nature of the critical...
 4.2.13: In Exercises 320, identify and determine the nature of the critical...
 4.2.14: In Exercises 320, identify and determine the nature of the critical...
 4.2.15: In Exercises 320, identify and determine the nature of the critical...
 4.2.16: In Exercises 320, identify and determine the nature of the critical...
 4.2.17: In Exercises 320, identify and determine the nature of the critical...
 4.2.18: In Exercises 320, identify and determine the nature of the critical...
 4.2.19: In Exercises 320, identify and determine the nature of the critical...
 4.2.20: In Exercises 320, identify and determine the nature of the critical...
 4.2.21: (a) Find all critical points of f (x, y) = 2y3 3y2 36y + 2 1 + 3x 2...
 4.2.22: (a) Under what conditions on the constant k will the function f (x,...
 4.2.23: (a) Consider the function f (x, y) = ax 2 + by2, where a and b are ...
 4.2.24: Sometimes it can be difficult to determine the critical point of a ...
 4.2.25: Sometimes it can be difficult to determine the critical point of a ...
 4.2.26: Sometimes it can be difficult to determine the critical point of a ...
 4.2.27: Sometimes it can be difficult to determine the critical point of a ...
 4.2.28: Show that the largest rectangular box having a fixed surface area m...
 4.2.29: What point on the plane 3x 4y z = 24 is closest to the origin?
 4.2.30: Find the points on the surface x y + z2 = 4 that are closest to the...
 4.2.31: Suppose that you are in charge of manufacturing two types of televi...
 4.2.32: Find the absolute extrema of f (x, y) = x 2 + x y + y2 6y on the re...
 4.2.33: Find the absolute maximum and minimum of f (x, y,z) = x 2 + x z y2 ...
 4.2.34: A metal plate has the shape of the region x 2 + y2 1. The plate is ...
 4.2.35: Find the (absolute) maximum and minimum values of f (x, y) = sin x ...
 4.2.36: Find the absolute extrema of f (x, y) = 2 cos x + 3 sin y on the re...
 4.2.37: Determine the absolute minimum and maximum values of the function f...
 4.2.38: Determine the absolute minimum and maximum values of the function f...
 4.2.39: Find the absolute extrema of f (x, y,z) = e1x2y2+2yz24z on the ball...
 4.2.40: Each of the functions in Exercises 4045 has a critical point at the...
 4.2.41: Each of the functions in Exercises 4045 has a critical point at the...
 4.2.42: Each of the functions in Exercises 4045 has a critical point at the...
 4.2.43: Each of the functions in Exercises 4045 has a critical point at the...
 4.2.44: Each of the functions in Exercises 4045 has a critical point at the...
 4.2.45: Each of the functions in Exercises 4045 has a critical point at the...
 4.2.46: In Exercises 4648, (a) find all critical points of the given functi...
 4.2.47: In Exercises 4648, (a) find all critical points of the given functi...
 4.2.48: In Exercises 4648, (a) find all critical points of the given functi...
 4.2.49: Determine the global extrema, if any, of f (x, y) = x y + 2y ln x 2...
 4.2.50: Find all local and global extrema of the function f (x, y,z) = x 3 ...
 4.2.51: Let f (x, y) = 3 [(x 1)(y 2)] 2/3 . (a) Determine all critical poin...
 4.2.52: (a) Suppose f : R R is a differentiable function of a single variab...
 4.2.53: (a) Let f be a continuous function of one variable. Show that if f ...
Solutions for Chapter 4.2: Extrema of Functions
Full solutions for Vector Calculus  4th Edition
ISBN: 9780321780652
Solutions for Chapter 4.2: Extrema of Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Since 53 problems in chapter 4.2: Extrema of Functions have been answered, more than 12500 students have viewed full stepbystep solutions from this chapter. Chapter 4.2: Extrema of Functions includes 53 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Vector Calculus was written by and is associated to the ISBN: 9780321780652.

Amplitude
See Sinusoid.

Angle of depression
The acute angle formed by the line of sight (downward) and the horizontal

Center
The central point in a circle, ellipse, hyperbola, or sphere

Commutative properties
a + b = b + a ab = ba

Distance (on a number line)
The distance between real numbers a and b, or a  b

Magnitude of an arrow
The magnitude of PQ is the distance between P and Q

Newton’s law of cooling
T1t2 = Tm + 1T0  Tm2ekt

Nonsingular matrix
A square matrix with nonzero determinant

Open interval
An interval that does not include its endpoints.

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

Pole
See Polar coordinate system.

Positive linear correlation
See Linear correlation.

Quartic regression
A procedure for fitting a quartic function to a set of data.

Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.

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

Real zeros
Zeros of a function that are real numbers.

Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.

Right triangle
A triangle with a 90° angle.

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.