 3.2.1: In Exercises 14, explain why Rolles Theorem does not apply to the f...
 3.2.2: In Exercises 14, explain why Rolles Theorem does not apply to the f...
 3.2.3: In Exercises 14, explain why Rolles Theorem does not apply to the f...
 3.2.4: In Exercises 14, explain why Rolles Theorem does not apply to the f...
 3.2.5: In Exercises 58, find the two intercepts of the function and show ...
 3.2.6: In Exercises 58, find the two intercepts of the function and show ...
 3.2.7: In Exercises 58, find the two intercepts of the function and show ...
 3.2.8: In Exercises 58, find the two intercepts of the function and show ...
 3.2.9: Rolles Theorem In Exercises 9 and 10, the graph of is shown. Apply ...
 3.2.10: Rolles Theorem In Exercises 9 and 10, the graph of is shown. Apply ...
 3.2.11: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.12: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.13: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.14: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.15: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.16: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.17: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.18: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.19: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.20: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.21: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.22: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.23: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.24: In Exercises 1124, determine whether Rolles Theorem can be applied ...
 3.2.25: In Exercises 2528, use a graphing utility to graph the function on ...
 3.2.26: In Exercises 2528, use a graphing utility to graph the function on ...
 3.2.27: In Exercises 2528, use a graphing utility to graph the function on ...
 3.2.28: In Exercises 2528, use a graphing utility to graph the function on ...
 3.2.29: Vertical Motion The height of a ball seconds after it is thrown upw...
 3.2.30: Reorder Costs The ordering and transportation cost for components u...
 3.2.31: In Exercises 31 and 32, copy the graph and sketch the secant line t...
 3.2.32: In Exercises 31 and 32, copy the graph and sketch the secant line t...
 3.2.33: Writing In Exercises 3336, explain why the Mean Value Theorem does ...
 3.2.34: Writing In Exercises 3336, explain why the Mean Value Theorem does ...
 3.2.35: Writing In Exercises 3336, explain why the Mean Value Theorem does ...
 3.2.36: Writing In Exercises 3336, explain why the Mean Value Theorem does ...
 3.2.37: Mean Value Theorem Consider the graph of the function (a) Find the ...
 3.2.38: Mean Value Theorem Consider the graph of the function (a) Find the ...
 3.2.39: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.40: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.41: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.42: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.43: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.44: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.45: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.46: In Exercises 39 46, determine whether the Mean Value Theorem can be...
 3.2.47: In Exercises 47 50, use a graphing utility to (a) graph the functio...
 3.2.48: In Exercises 47 50, use a graphing utility to (a) graph the functio...
 3.2.49: In Exercises 47 50, use a graphing utility to (a) graph the functio...
 3.2.50: In Exercises 47 50, use a graphing utility to (a) graph the functio...
 3.2.51: Vertical Motion The height of an object seconds after it is dropped...
 3.2.52: Sales A company introduces a new product for which the number of un...
 3.2.53: Let be continuous on and differentiable on If there exists in such ...
 3.2.54: Let be continuous on the closed interval and differentiable on the ...
 3.2.55: The function is differentiable on and satisfies However, its deriva...
 3.2.56: Can you find a function such that f2 6, and for all Why or why not?...
 3.2.57: Speed A plane begins its takeoff at 2:00 P.M. on a 2500mile flight...
 3.2.58: Temperature When an object is removed from a furnace and placed in ...
 3.2.59: Velocity Two bicyclists begin a race at 8:00 A.M. They both finish ...
 3.2.60: Acceleration At 9:13 A.M., a sports car is traveling 35 miles per h...
 3.2.61: Graphical Reasoning The figure shows two parts of the graph of a co...
 3.2.62: Consider the function (a) Use a graphing utility to graph and (b) I...
 3.2.63: Think About It In Exercises 63 and 64, sketch the graph of an arbit...
 3.2.64: Think About It In Exercises 63 and 64, sketch the graph of an arbit...
 3.2.65: In Exercises 65 and 66, use the Intermediate Value Theorem and Roll...
 3.2.66: In Exercises 65 and 66, use the Intermediate Value Theorem and Roll...
 3.2.67: Determine the values and such that the function satisfies the hypot...
 3.2.68: Determine the values and so that the function satisfies the hypothe...
 3.2.69: Differential Equations In Exercises 6972, find a function that has ...
 3.2.70: Differential Equations In Exercises 6972, find a function that has ...
 3.2.71: Differential Equations In Exercises 6972, find a function that has ...
 3.2.72: Differential Equations In Exercises 6972, find a function that has ...
 3.2.73: True or False? In Exercises 7376, determine whether the statement i...
 3.2.74: True or False? In Exercises 7376, determine whether the statement i...
 3.2.75: True or False? In Exercises 7376, determine whether the statement i...
 3.2.76: True or False? In Exercises 7376, determine whether the statement i...
 3.2.77: Prove that if and is any positive integer, then the polynomial func...
 3.2.78: Prove that if for all in an interval then is constant on xy
 3.2.79: Let Prove that for any interval the value guaranteed by the Mean Va...
 3.2.80: (a) Let and Then and Show that there is at least one value in the i...
 3.2.81: Prove that if is differentiable on and for all real numbers, then h...
 3.2.82: Use the result of Exercise 81 to show that has at most one fixed po...
 3.2.83: Prove that for all and 10x21
 3.2.84: Prove that for all and x21y
 3.2.85: Let Use the Mean Value Theorem to show that 21y
Solutions for Chapter 3.2: Rolles Theorem and the Mean Value Theorem
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 3.2: Rolles Theorem and the Mean Value Theorem
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.2: Rolles Theorem and the Mean Value Theorem includes 85 full stepbystep solutions. Since 85 problems in chapter 3.2: Rolles Theorem and the Mean Value Theorem have been answered, more than 71156 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus, edition: 8. Calculus was written by and is associated to the ISBN: 9780618502981.

Boxplot (or boxandwhisker plot)
A graph that displays a fivenumber summary

Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian threedimensional space

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Index
See Radical.

Integrable over [a, b] Lba
ƒ1x2 dx exists.

Logarithm
An expression of the form logb x (see Logarithmic function)

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Multiplicative inverse of a matrix
See Inverse of a matrix

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Onetoone rule of exponents
x = y if and only if bx = by.

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Positive association
A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

Statute mile
5280 feet.

symmetric about the xaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

System
A set of equations or inequalities.

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.

Vertex of an angle
See Angle.