 4.2.1: 1 4 Verify that the function satisfies the three hypotheses of Roll...
 4.2.2: 1 4 Verify that the function satisfies the three hypotheses of Roll...
 4.2.3: 1 4 Verify that the function satisfies the three hypotheses of Roll...
 4.2.4: 1 4 Verify that the function satisfies the three hypotheses of Roll...
 4.2.5: Let . Show that but there is no number in such that . Why does this...
 4.2.6: Let . Show that but there is no number in such that . Why does this...
 4.2.7: Use the graph of to estimate the values of that satisfy the conclus...
 4.2.8: Use the graph of given in Exercise 7 to estimate the values of that...
 4.2.9: 912 Verify that the function satisfies the hypotheses of the Mean V...
 4.2.10: 912 Verify that the function satisfies the hypotheses of the Mean V...
 4.2.11: 912 Verify that the function satisfies the hypotheses of the Mean V...
 4.2.12: 912 Verify that the function satisfies the hypotheses of the Mean V...
 4.2.13: 1314 Find the number that satisfies the conclusion of the Mean Valu...
 4.2.14: 1314 Find the number that satisfies the conclusion of the Mean Valu...
 4.2.15: Let . Show that there is no value of in such that . Why does this n...
 4.2.16: . Let . Show that there is no value of such that . Why does this no...
 4.2.17: 1718 Show that the equation has exactly one real root.2x cos x 0 x
 4.2.18: 1718 Show that the equation has exactly one real root.x 3 e 2
 4.2.19: Show that the equation has at most one root in the interval .
 4.2.20: Show that the equation has at most two real roots.
 4.2.21: (a) Show that a polynomial of degree 3 has at most three real roots...
 4.2.22: (a) Suppose that is differentiable on and has two roots. Show that ...
 4.2.23: If and for , how small can possibly be?
 4.2.24: Suppose that for all values of . Show that18 f8 f2 303 f
 4.2.25: Does there exist a function such that , , and for all ?
 4.2.26: Suppose that and are continuous on and differenti able on . Suppose...
 4.2.27: Show that s1 x 1 x 0 12
 4.2.28: Suppose is an odd function and is differentiable everywhere. Prove ...
 4.2.29: Use the Mean Value Theorem to prove the inequality for all a and b ...
 4.2.30: If (c a constant) for all , use Corollary 7 to show that for some c...
 4.2.31: Let and Show that for all in their domains. Can we conclude from Co...
 4.2.32: Use the method of Example 6 to prove the identity
 4.2.33: Prove the identity
 4.2.34: At 2:00 PM a cars speedometer reads 30 mih. At 2:10 PM it reads 50 ...
 4.2.35: Two runners start a race at the same time and finish in a tie. Prov...
 4.2.36: . A number a is called a fixed point of a function if . Prove that ...
Solutions for Chapter 4.2: The Mean Value Theorem
Full solutions for Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
Solutions for Chapter 4.2: The Mean Value Theorem
Get Full SolutionsSince 36 problems in chapter 4.2: The Mean Value Theorem have been answered, more than 29624 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. Chapter 4.2: The Mean Value Theorem includes 36 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909.

Arcsecant function
See Inverse secant function.

Complements or complementary angles
Two angles of positive measure whose sum is 90°

Compounded annually
See Compounded k times per year.

Constant of variation
See Power function.

Convergence of a sequence
A sequence {an} converges to a if limn: q an = a

Degree
Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Irrational zeros
Zeros of a function that are irrational numbers.

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

Order of magnitude (of n)
log n.

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Positive angle
Angle generated by a counterclockwise rotation.

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

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.

Stem
The initial digit or digits of a number in a stemplot.

Sum of an infinite geometric series
Sn = a 1  r , r 6 1

Translation
See Horizontal translation, Vertical translation.

Vertical line test
A test for determining whether a graph is a function.

Whole numbers
The numbers 0, 1, 2, 3, ... .