 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 and is associated to the ISBN: 9780470888612. Since 64 problems in chapter 4.4: FAMILIES OF FUNCTIONS AND MODELING have been answered, more than 29776 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Compound interest
Interest that becomes part of the investment

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

Explanatory variable
A variable that affects a response variable.

Fivenumber summary
The minimum, first quartile, median, third quartile, and maximum of a data set.

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

Inverse relation (of the relation R)
A relation that consists of all ordered pairs b, a for which a, b belongs to R.

Irrational zeros
Zeros of a function that are irrational numbers.

Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Partial fraction decomposition
See Partial fractions.

Polar equation
An equation in r and ?.

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Radicand
See Radical.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Terminal side of an angle
See Angle.

Venn diagram
A visualization of the relationships among events within a sample space.

xintercept
A point that lies on both the graph and the xaxis,.

yzplane
The points (0, y, z) in Cartesian space.