 3.1: Explain why or why not Determine whether the following statements a...
 3.2: 25. Slopes and tangent lines from the definition f 1x2 = 4x2  7x +...
 3.3: 25. Slopes and tangent lines from the definition f 1x2 = 5x3 + x; P...
 3.4: 25. Slopes and tangent lines from the definition f 1x2 = x + 3 2x +...
 3.5: 25. Slopes and tangent lines from the definition f 1x2 = 1 223x + 1...
 3.6: Calculating average and instantaneous velocities Suppose the height...
 3.7: Population of the United States The population of the United States...
 3.8: Growth rate of bacteria Suppose the following graph represents the ...
 3.9: Velocity of a skydiver Assume the graph represents the distance (in...
 3.10: 1011. Using the definition of the derivative Use the definition of ...
 3.11: 1011. Using the definition of the derivative Use the definition of ...
 3.12: Sketching a derivative graph Sketch a graph of f _ for the function...
 3.13: Sketching a derivative graph Sketch a graph of g_ for the function ...
 3.14: Matching functions and derivatives Match the functions in ad with t...
 3.15: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.16: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.17: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.18: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.19: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.20: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.21: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.22: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.23: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.24: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.25: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.26: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.27: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.28: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.29: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.30: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.31: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.32: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.33: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.34: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.35: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.36: 1536. Evaluating derivatives Evaluate and simplify the following de...
 3.37: 3739. Implicit differentiation Calculate y1x2 for the following rel...
 3.38: 3739. Implicit differentiation Calculate y1x2 for the following rel...
 3.39: 3739. Implicit differentiation Calculate y1x2 for the following rel...
 3.40: Quadratic functions a. Show that if 1a, f 1a22 is any point on the ...
 3.41: 4144. Tangent lines Find an equation of the line tangent to the fol...
 3.42: 4144. Tangent lines Find an equation of the line tangent to the fol...
 3.43: 4144. Tangent lines Find an equation of the line tangent to the fol...
 3.44: 4144. Tangent lines Find an equation of the line tangent to the fol...
 3.45: Horizontal/vertical tangent lines For what value(s) of x is the lin...
 3.46: A parabola property Let f 1x2 = x2. a. Show that f 1x2  f 1y2 x  ...
 3.47: 4748. Higherorder derivatives Find y, y, and y for the following f...
 3.48: 4748. Higherorder derivatives Find y, y, and y for the following f...
 3.49: 4952. Derivative formulas Evaluate the following derivatives. Expre...
 3.50: 4952. Derivative formulas Evaluate the following derivatives. Expre...
 3.51: 4952. Derivative formulas Evaluate the following derivatives. Expre...
 3.52: 4952. Derivative formulas Evaluate the following derivatives. Expre...
 3.53: Finding derivatives from a table Find the values of the following d...
 3.54: 5455. Limits The following limits represent the derivative of a fun...
 3.55: 5455. Limits The following limits represent the derivative of a fun...
 3.56: 5657. Derivative of the inverse at a point Consider the following f...
 3.57: 5657. Derivative of the inverse at a point Consider the following f...
 3.58: 5859. Derivative of the inverse Find the derivative of the inverse ...
 3.59: 5859. Derivative of the inverse Find the derivative of the inverse ...
 3.60: A function and its inverse function The function f 1x2 = x x + 1 is...
 3.61: Derivative of the inverse in two ways Let f 1x2 = sin x, f 1 1x2 =...
 3.62: 6263. Derivatives from a graph If possible, evaluate the following ...
 3.63: 6263. Derivatives from a graph If possible, evaluate the following ...
 3.64: Velocity of a probe A small probe is launched vertically from the g...
 3.65: Marginal and average cost Suppose the cost of producing x lawn mowe...
 3.66: Marginal and average cost Suppose a company produces fly rods. Assu...
 3.67: Population growth Suppose p1t2 = 1.7t3 + 72t2 + 7200t + 80,000 is ...
 3.68: Position of a piston The distance between the head of a piston and ...
 3.69: Boat rates Two boats leave a dock at the same time. One boat travel...
 3.70: Rate of inflation of a balloon A spherical balloon is inflated at a...
 3.71: Rate of descent of a hotair balloon A rope is attached to the bott...
 3.72: Filling a tank Water flows into a conical tank at a rate of 2 ft3>m...
 3.73: Angle of elevation A jet flies horizontally 500 ft directly above a...
 3.74: Viewing angle A man whose eye level is 6 ft above the ground walks ...
Solutions for Chapter 3: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 3
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. Chapter 3 includes 74 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 74 problems in chapter 3 have been answered, more than 49150 students have viewed full stepbystep solutions from this chapter.

Absolute minimum
A value ƒ(c) is an absolute minimum value of ƒ if ƒ(c) ? ƒ(x)for all x in the domain of ƒ.

Completing the square
A method of adding a constant to an expression in order to form a perfect square

Components of a vector
See Component form of a vector.

Convenience sample
A sample that sacrifices randomness for convenience

Coordinate plane
See Cartesian coordinate system.

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

Direction angle of a vector
The angle that the vector makes with the positive xaxis

Divergence
A sequence or series diverges if it does not converge

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Local extremum
A local maximum or a local minimum

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Onetoone function
A function in which each element of the range corresponds to exactly one element in the domain

Parametric equations for a line in space
The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

Standard position (angle)
An angle positioned on a rectangular coordinate system with its vertex at the origin and its initial side on the positive xaxis

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.