 4.2.1E: Checking the Mean Value TheoremFind the value or values of c that s...
 4.2.2E: Checking the Mean Value TheoremFind the value or values of c that s...
 4.2.3E: Checking the Mean Value TheoremFind the value or values of c that s...
 4.2.4E: Checking the Mean Value TheoremFind the value or values of c that s...
 4.2.5E: Checking the Mean Value TheoremFind the value or values of c that s...
 4.2.6E: Checking the Mean Value TheoremFind the value or values of c that s...
 4.2.7E: Checking the Mean Value TheoremFind the value or values of c that s...
 4.2.8E: Checking the Mean Value TheoremFind the value or values of c that s...
 4.2.9E: Checking the Mean Value TheoremWhich of the functions satisfy the h...
 4.2.10E: Checking the Mean Value TheoremWhich of the functions satisfy the h...
 4.2.11E: Checking the Mean Value TheoremWhich of the functions satisfy the h...
 4.2.12E: Checking the Mean Value TheoremWhich of the functions satisfy the h...
 4.2.13E: Checking the Mean Value TheoremWhich of the functions satisfy the h...
 4.2.14E: Checking the Mean Value TheoremWhich of the functions satisfy the h...
 4.2.15E: Checking the Mean Value TheoremThe function is zero at x = 0 1and x...
 4.2.16E: Checking the Mean Value TheoremFor what values of a, m, and b does ...
 4.2.17E: a. Plot the zeros of each polynomial on a line together with the ze...
 4.2.18E: Suppose that f '' is continuous on [a, b] and that ƒ has three zero...
 4.2.19E: Show that if f '' > 0 throughout an interval [a, b], then f ' has a...
 4.2.20E: Show that a cubic polynomial can have at most three real zeros.
 4.2.21E: Show that the functions have exactly one zero in the given interval.
 4.2.22E: Show that the functions have exactly one zero in the given interval.
 4.2.23E: Show that the functions have exactly one zero in the given interval.
 4.2.24E: Show that the functions have exactly one zero in the given interval.
 4.2.25E: Show that the functions have exactly one zero in the given interval.
 4.2.26E: Show that the functions have exactly one zero in the given interval.
 4.2.27E: Show that the functions have exactly one zero in the given interval.
 4.2.28E: Show that the functions have exactly one zero in the given interval.
 4.2.29E: Finding Functions from DerivativesSuppose that and that for all x. ...
 4.2.30E: Finding Functions from DerivativesSuppose that for all x. Must ƒ(x)...
 4.2.31E: Finding Functions from DerivativesSuppose that for all x. Find ƒ(2) if
 4.2.32E: Finding Functions from DerivativesWhat can be said about functions ...
 4.2.33E: Finding Functions from DerivativesFind all possible functions with ...
 4.2.34E: Finding Functions from DerivativesFind all possible functions with ...
 4.2.35E: Finding Functions from DerivativesFind all possible functions with ...
 4.2.36E: Finding Functions from DerivativesFind all possible functions with ...
 4.2.37E: Finding Functions from DerivativesFind all possible functions with ...
 4.2.38E: Finding Functions from DerivativesFind all possible functions with ...
 4.2.39E: Finding Functions from DerivativesFind the function with the given ...
 4.2.40E: Finding Functions from DerivativesFind the function with the given ...
 4.2.41E: Finding Functions from DerivativesFind the function with the given ...
 4.2.42E: Finding Functions from DerivativesFind the function with the given ...
 4.2.43E: Finding Position from Velocity or AccelerationGive the velocity and...
 4.2.44E: Finding Position from Velocity or AccelerationGive the velocity and...
 4.2.45E: Finding Position from Velocity or AccelerationGive the velocity and...
 4.2.46E: Finding Position from Velocity or AccelerationGive the velocity and...
 4.2.47E: Finding Position from Velocity or AccelerationGive the acceleration...
 4.2.48E: Finding Position from Velocity or AccelerationGive the acceleration...
 4.2.49E: Finding Position from Velocity or AccelerationGive the acceleration...
 4.2.50E: Finding Position from Velocity or AccelerationGive the acceleration...
 4.2.51E: ApplicationsTemperature changeIt took 14 sec for a mercury thermome...
 4.2.52E: ApplicationsA trucker handed in a ticket at a toll booth showing th...
 4.2.53E: ApplicationsClassical accounts tell us that a 170oar trireme (anci...
 4.2.54E: ApplicationsA marathoner ran the 26.2mi New York City Marathon in ...
 4.2.55E: ApplicationsShow that at some instant during a 2hour automobile tr...
 4.2.56E: ApplicationsFree fall on the moon On our moon, the acceleration of ...
 4.2.57E: Theory and ExamplesThe geometric mean of a and b The geometric mean...
 4.2.58E: Theory and ExamplesThe arithmetic mean of a and b The arithmetic me...
 4.2.59E: Theory and ExamplesGraph the function What does the graph do? Why d...
 4.2.60E: Theory and ExamplesRolle’s Theorema. Construct a polynomial ƒ(x) th...
 4.2.61E: Theory and ExamplesUnique solution Assume that ƒ is continuous on [...
 4.2.62E: Theory and ExamplesParallel tangents Assume that ƒ and g are differ...
 4.2.63E: Theory and ExamplesSuppose that Show that ƒ(4)  ƒ(1) ? 3
 4.2.64E: Theory and ExamplesSuppose that 0 < f’(x) < ½ for all x  values. S...
 4.2.65E: Theory and ExamplesShow that for all xvalues. (Hint: Consider on .)
 4.2.66E: Theory and ExamplesShow that for any numbers a and b, the sine ineq...
 4.2.67E: Theory and ExamplesIf the graphs of two differentiable functions ƒ(...
 4.2.68E: Theory and ExamplesIf for all values w and x and ƒ is a differentia...
 4.2.69E: Theory and ExamplesAssume that ƒ is differentiable on Show that is ...
 4.2.70E: Theory and ExamplesLet ƒ be a function defined on an interval [a, b...
 4.2.71E: Theory and ExamplesUse the inequalities in Exercise 70 to estimate ...
 4.2.72E: Theory and ExamplesUse the inequalities in Exercise 70 to estimate ...
 4.2.73E: Theory and ExamplesLet ƒ be differentiable at every value of x and ...
 4.2.74E: Theory and ExamplesLet be a quadratic function defined on a closed ...
 4.2.75E: Theory and ExamplesUse the samederivative argument, as was done to...
 4.2.76E: Theory and ExamplesUse the samederivative argument to prove the id...
 4.2.77E: Theory and ExamplesStarting with the equation derived in the text, ...
 4.2.78E: Theory and ExamplesShow that for any numbers x1 and x2
Solutions for Chapter 4.2: Thomas' Calculus: Early Transcendentals 13th Edition
Full solutions for Thomas' Calculus: Early Transcendentals  13th Edition
ISBN: 9780321884077
Solutions for Chapter 4.2
Get Full SolutionsChapter 4.2 includes 78 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13. Since 78 problems in chapter 4.2 have been answered, more than 88519 students have viewed full stepbystep solutions from this chapter. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077.

Coterminal angles
Two angles having the same initial side and the same terminal side

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

Factoring (a polynomial)
Writing a polynomial as a product of two or more polynomial factors.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Index of summation
See Summation notation.

Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative

Numerical model
A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

Parametric curve
The graph of parametric equations.

Pie chart
See Circle graph.

Polar coordinate system
A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Random behavior
Behavior that is determined only by the laws of probability.

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).

Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

Reference angle
See Reference triangle

Row operations
See Elementary row operations.

Singular matrix
A square matrix with zero determinant

Transformation
A function that maps real numbers to real numbers.