 2.1: Explain the difference between average and instantaneous rates of c...
 2.2: In parts (a)(d), use the function y = 12 x2.(a) Find the average ra...
 2.3: Complete each part for the function f(x) = x2 + 1.(a) Find the slop...
 2.4: A car is traveling on a straight road that is 120 mi long. Forthe f...
 2.5: At time t = 0 a car moves into the passing lane to pass aslowmovin...
 2.6: A skydiver jumps from an airplane. Suppose that the distanceshe fal...
 2.7: A particle moves on a line away from its initial positionso that af...
 2.8: State the definition of a derivative, and give two interpretations ...
 2.9: Use the definition of a derivative to find dy/dx, and checkyour ans...
 2.10: Suppose that f(x) =x2 1, x 1k(x 1), x > 1.For what values of k is f...
 2.11: The accompanying figure shows the graph of y = f (x) foran unspecif...
 2.12: Sketch the graph of a function f for which f(0) = 1,f (0) = 0, f (x...
 2.13: According to the U.S. Bureau of the Census, the estimatedand projec...
 2.14: Use a graphing utility to graph the functionf(x) = x4 x 1 xand es...
 2.15: 1518 (a) Use a CAS to find f (x) via Definition 2.2.1; (b) check th...
 2.16: 1518 (a) Use a CAS to find f (x) via Definition 2.2.1; (b) check th...
 2.17: 1518 (a) Use a CAS to find f (x) via Definition 2.2.1; (b) check th...
 2.18: 1518 (a) Use a CAS to find f (x) via Definition 2.2.1; (b) check th...
 2.19: The amount of water in a tank t minutes after it has startedto drai...
 2.20: Use the formula V = l3 for the volume of a cube of side lto find(a)...
 2.21: 2122 Zoom in on the graph of f on an interval containing x = x0 unt...
 2.22: 2122 Zoom in on the graph of f on an interval containing x = x0 unt...
 2.23: Suppose that a function f is differentiable at x = 1 andlimh0f(1 + ...
 2.24: Suppose that a function f is differentiable at x = 2 andlimx2x3f(x)...
 2.25: Find the equations of all lines through the origin that aretangent ...
 2.26: Find all values of x for which the tangent line to the curvey = 2x3...
 2.27: Let f(x) = x2. Show that for any distinct values of a andb, the slo...
 2.28: In each part, evaluate the expression given that f(1) = 1,g(1) = 2,...
 2.29: 2932 Find f (x). (a) f(x) = x8 3x + 5x3(b) f(x) = (2x + 1)101(5x2 7)
 2.30: 2932 Find f (x). (a) f(x) = sin x + 2 cos3 x(b) f(x) = (1 + sec x)(...
 2.31: 2932 Find f (x). (a) f(x) = 3x + 1(x 1)2(b) f(x) =3x + 1x23
 2.32: 2932 Find f (x). (a) f(x) = cot csc 2xx3 + 5(b) f(x) = 12x + sin3 x33
 2.33: 3334 Find the values of x at which the curve y = f(x) has a horizon...
 2.34: 3334 Find the values of x at which the curve y = f(x) has a horizon...
 2.35: Find all lines that are simultaneously tangent to the graphof y = x...
 2.36: (a) Let n denote an even positive integer. Generalize theresult of ...
 2.37: Find all values of x for which the line that is tangent toy = 3x ta...
 2.38: Approximate the values of x at which the tangent line to thegraph o...
 2.39: Suppose that f(x) = M sin x + N cos x for some constantsM and N. If...
 2.40: Suppose that f(x) = M tan x + N sec x for some constantsM and N. If...
 2.41: Suppose that f (x) = 2x f(x) and f(2) = 5.(a) Find g(/3) if g(x) = ...
Solutions for Chapter 2: THE DERIVATIVE
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 2: THE DERIVATIVE
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2: THE DERIVATIVE includes 41 full stepbystep solutions. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Since 41 problems in chapter 2: THE DERIVATIVE have been answered, more than 38114 students have viewed full stepbystep solutions from this chapter.

Chord of a conic
A line segment with endpoints on the conic

Combinatorics
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

End behavior
The behavior of a graph of a function as.

Explanatory variable
A variable that affects a response variable.

Finite series
Sum of a finite number of terms.

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Index of summation
See Summation notation.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Inverse composition rule
The composition of a onetoone function with its inverse results in the identity function.

Inverse cotangent function
The function y = cot1 x

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Partial fractions
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

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

Solve graphically
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Summation notation
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

System
A set of equations or inequalities.

Time plot
A line graph in which time is measured on the horizontal axis.

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.