 4.4.1: In Exercises 16, investigate the oneparameter family offunctions. ...
 4.4.2: In Exercises 16, investigate the oneparameter family offunctions. ...
 4.4.3: In Exercises 16, investigate the oneparameter family offunctions. ...
 4.4.4: In Exercises 16, investigate the oneparameter family offunctions. ...
 4.4.5: In Exercises 16, investigate the oneparameter family offunctions. ...
 4.4.6: In Exercises 16, investigate the oneparameter family offunctions. ...
 4.4.7: Consider the familyy = Ax + B .(a) If B = 0, what is the effect of ...
 4.4.8: If A and B are positive constants, find all critical pointsoff(w) =...
 4.4.9: The graphs of f(x)=1+ eax for a = 1, 2, and 5, arein Figure 4.63. W...
 4.4.10: The graphs of f(x) = xeax for a = 1, 2 , and 3, are inFigure 4.64. ...
 4.4.11: In Exercises 1116, investigate the given two parameter familyof fun...
 4.4.12: In Exercises 1116, investigate the given two parameter familyof fun...
 4.4.13: In Exercises 1116, investigate the given two parameter familyof fun...
 4.4.14: In Exercises 1116, investigate the given two parameter familyof fun...
 4.4.15: In Exercises 1116, investigate the given two parameter familyof fun...
 4.4.16: In Exercises 1116, investigate the given two parameter familyof fun...
 4.4.17: The graphs of the function f(x) = x + a2/x for a = 1and 2, and a th...
 4.4.18: The graphs of the function f(x) = x + a sin x for variousvalues of ...
 4.4.19: (a) Sketch graphs of y = xebx for b = 1, 2, 3, 4. Describethe graph...
 4.4.20: Consider the surge function y = axebx for a, b > 0.(a) Find the loc...
 4.4.21: Find a formula for the family of cubic polynomials withan inflectio...
 4.4.22: (a) Derive formulas for the first and second derivativesof the logi...
 4.4.23: (a) Graph f(x) = x + a sin x for a = 0.5 and a = 3.(b) For what val...
 4.4.24: (a) Graph f(x) = x2 + a sin x for a = 1 and a = 20.(b) For what val...
 4.4.25: Consider the family of functions y = a cosh(x/a) fora > 0. Sketch g...
 4.4.26: Sketch several members of the family y = eax sin bxfor b = 1, and d...
 4.4.27: Sketch several members of the family eax sin bx fora = 1, and descr...
 4.4.28: If a > 0, b > 0, show that f(x) = a(1 ebx) is everywhereincreasing ...
 4.4.29: Let f(x) = bxe1+bx, where b is constant and b > 0.(a) What is the x...
 4.4.30: Let h(x) = ex +kx, where k is any constant. For whatvalue(s) of k d...
 4.4.31: Let g(x) = x kex, where k is any constant. For whatvalue(s) of k do...
 4.4.32: Find formulas for the functions described in 3243.A function of the...
 4.4.33: Find formulas for the functions described in 3243.A function of the...
 4.4.34: Find formulas for the functions described in 3243.A curve of the fo...
 4.4.35: Find formulas for the functions described in 3243.A logistic curve ...
 4.4.36: Find formulas for the functions described in 3243.A function of the...
 4.4.37: Find formulas for the functions described in 3243.A cubic polynomia...
 4.4.38: Find formulas for the functions described in 3243.A fourthdegree p...
 4.4.39: Find formulas for the functions described in 3243.A function of the...
 4.4.40: Find formulas for the functions described in 3243.A function of the...
 4.4.41: Find formulas for the functions described in 3243.A function of the...
 4.4.42: Find formulas for the functions described in 3243.A function of the...
 4.4.43: Find formulas for the functions described in 3243.A function of the...
 4.4.44: Consider the family of functions y = f(x) = x kx,with k a positive ...
 4.4.45: For any constant a, let f(x) = ax x ln x for x > 0.(a) What is the ...
 4.4.46: Let f(x) = x2 + cos(kx), for k > 0.(a) Graph f for k = 0.5, 1, 3, 5...
 4.4.47: Let f(x) = ex kx, for k > 0.(a) Graph f for k = 1/4, 1/2, 1, 2, 4. ...
 4.4.48: A family of functions is given byr(x) = 1a + (x b)2 .(a) For what v...
 4.4.49: (a) Find all critical points of f(x) = x4 + ax2 + b.(b) Under what ...
 4.4.50: Let y = Aex + Bex for any constants A, B.(a) Sketch the graph of th...
 4.4.51: The temperature, T , in C, of a yam put into a 200Coven is given as...
 4.4.52: For positive a, b, the potential energy, U, of a particle isU = ba2...
 4.4.53: The force, F, on a particle with potential energy U isgiven byF = d...
 4.4.54: The LennardJones model predicts the potential energyV (r) of a two...
 4.4.55: For positive A, B, the force between two atoms is a functionof the ...
 4.4.56: An organism has size W at time t. For positive constantsA, b, and c...
 4.4.57: In 5758, explain what is wrong with the statement.Every function of...
 4.4.58: In 5758, explain what is wrong with the statement.Every function of...
 4.4.59: In 5962, give an example of:A family of quadratic functions which h...
 4.4.60: In 5962, give an example of:A member of the family f(x) = ax3 bx th...
 4.4.61: In 5962, give an example of:A family of functions, f(x), depending ...
 4.4.62: In 5962, give an example of:A family of functions, g(x), depending ...
 4.4.63: Let f(x) = ax+b/x. Suppose a and b are positive. Whathappens to f(x...
 4.4.64: Let f(x) = ax+b/x. Suppose a and b are positive. Whathappens to f(x...
Solutions for Chapter 4.4: FAMILIES OF FUNCTIONS AND MODELING
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 4.4: FAMILIES OF FUNCTIONS AND MODELING
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Chapter 4.4: FAMILIES OF FUNCTIONS AND MODELING includes 64 full stepbystep solutions. Calculus: Single and Multivariable was written by Patricia and is associated to the ISBN: 9780470888612. Since 64 problems in chapter 4.4: FAMILIES OF FUNCTIONS AND MODELING have been answered, more than 13157 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°

Bearing
Measure of the clockwise angle that the line of travel makes with due north

Compounded continuously
Interest compounded using the formula A = Pert

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Cube root
nth root, where n = 3 (see Principal nth root),

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Initial value of a function
ƒ 0.

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

Jump discontinuity at x a
limx:a  ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

Parameter interval
See Parametric equations.

Period
See Periodic function.

PH
The measure of acidity

Range (in statistics)
The difference between the greatest and least values in a data set.

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

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.

Scalar
A real number.

Vector
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

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