- 4.6.1E: Explain Rolle's Theorem with a sketch.
- 4.6.2E: Draw the graph of a function for which the conclusion of Rolle's Th...
- 4.6.3E: Explain why Rolle's Theorem cannot be applied to the func ? ti?on? ...
- 4.6.4E: Explain the Mean Value Theorem with a sketch.
- 4.6.5E: Draw the graph of a function for which the conclusion of the Mean V...
- 4.6.6E: 3 At what po?ints c? does the conclusion of the Mean Value Theorem ...
- 4.6.22E: Mean Value Theorem a. Determine whether the Mean Value Theorem appl...
- 4.6.23E: Explain why or why not Determine whether the following statements a...
- 4.6.24E: Without evaluating derivatives which of the following functions hav...
- 4.6.25E: Without evaluating derivatives, which of the functions 10 10 10 10 ...
- 4.6.26E: Find all func?tions ?f whose derivative is f (x) = x+1.
- 4.6.27E: Mean Value Theorem and graphs ?By visual inspection, locate all poi...
- 4.6.28E: Avalanche forecasting ?Avalanche forecasters measure the ?temperatu...
- 4.6.29E: Mean Value Theorem and the police A sune patrol officer saw a car s...
- 4.6.30E: Mean Value Theorem and the police ?A slave patrol officer saw a car...
- 4.6.31E: Problem-31E Running pace ?Explain why if a runner completes a 6.2-m...
- 4.6.32AE: Mean Value Theorem for linear functions Interpret the Mean Value Th...
- 4.6.33AE: Mean Value Theorem for quadratic functions Consider the quadratic f...
- 4.6.34AE: Means 2 a. Show that the point c guaranteed to exist by the Mean Va...
- 4.6.35AE: 2 2 Equal derivatives Verify that the functions f(x) = tan xand g(x...
- 4.6.36AE: 2 2 Equal derivatives ?Verify that the functions f(x) = sin x and g...
- 4.6.37AE: 100-m speed ?The Jamaican sprinter Usain Bolt set a world record of...
- 4.6.38AE: Condition for non differentiability Suppose f (x) < 0 < f (x)for x ...
- 4.6.39AE: Generalized Mean Value Theorem ?Sup?pose f ? ? and? are functions t...
Solutions for Chapter 4.6: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals | 1st Edition
A rectangular graphical display of categorical data.
See Arithmetic sequence.
The function y = cos x
Direction vector for a line
A vector in the direction of a line in three-dimensional space
equation of an ellipse
(x - h2) a2 + (y - k)2 b2 = 1 or (y - k)2 a2 + (x - h)2 b2 = 1
A visible representation of a numerical or algebraic model.
The complex number.
Inverse composition rule
The composition of a one-toone function with its inverse results in the identity function.
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)
See Additive inverse of a real number and Additive inverse of a complex number.
Two lines that are both vertical or have equal slopes.
Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22 - 2r1r2 cos 1?1 - ?22
Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.
Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.
Zeros of a function that are rational numbers.
See Division algorithm for polynomials.
A real number.
Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series
The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a- ƒ1x2 = q.