 3.1.1: In Exercises 1 and 2, estimate the slope of the graph at the points...
 3.1.2: In Exercises 1 and 2, estimate the slope of the graph at the points...
 3.1.3: In Exercises 3 and 4, use the graph shown in the figure. To print a...
 3.1.4: In Exercises 3 and 4, use the graph shown in the figure. To print a...
 3.1.5: In Exercises 5 10, find the slope of the tangent line to the graph ...
 3.1.6: In Exercises 5 10, find the slope of the tangent line to the graph ...
 3.1.7: In Exercises 5 10, find the slope of the tangent line to the graph ...
 3.1.8: In Exercises 5 10, find the slope of the tangent line to the graph ...
 3.1.9: In Exercises 5 10, find the slope of the tangent line to the graph ...
 3.1.10: In Exercises 5 10, find the slope of the tangent line to the graph ...
 3.1.11: In Exercises 1124, find the derivative by the limit processfx 3 g
 3.1.12: In Exercises 1124, find the derivative by the limit processgx 5h
 3.1.13: In Exercises 1124, find the derivative by the limit processfx 5x fx
 3.1.14: In Exercises 1124, find the derivative by the limit processfx 3x 2f
 3.1.15: In Exercises 1124, find the derivative by the limit processhs 3 x 23sf
 3.1.16: In Exercises 1124, find the derivative by the limit process
 3.1.17: In Exercises 1124, find the derivative by the limit process
 3.1.18: In Exercises 1124, find the derivative by the limit processfx 1 x2 f
 3.1.19: In Exercises 1124, find the derivative by the limit processfx x3 12xf
 3.1.20: In Exercises 1124, find the derivative by the limit process
 3.1.21: In Exercises 1124, find the derivative by the limit process
 3.1.22: In Exercises 1124, find the derivative by the limit process
 3.1.23: In Exercises 1124, find the derivative by the limit process
 3.1.24: In Exercises 1124, find the derivative by the limit processfx 4x f
 3.1.25: In Exercises 2532, (a) find an equation of the tangent line to the ...
 3.1.26: In Exercises 2532, (a) find an equation of the tangent line to the ...
 3.1.27: In Exercises 2532, (a) find an equation of the tangent line to the ...
 3.1.28: In Exercises 2532, (a) find an equation of the tangent line to the ...
 3.1.29: In Exercises 2532, (a) find an equation of the tangent line to the ...
 3.1.30: In Exercises 2532, (a) find an equation of the tangent line to the ...
 3.1.31: In Exercises 2532, (a) find an equation of the tangent line to the ...
 3.1.32: In Exercises 2532, (a) find an equation of the tangent line to the ...
 3.1.33: In Exercises 3336, find an equation of the line that is tangent to ...
 3.1.34: In Exercises 3336, find an equation of the line that is tangent to ...
 3.1.35: In Exercises 3336, find an equation of the line that is tangent to ...
 3.1.36: In Exercises 3336, find an equation of the line that is tangent to ...
 3.1.37: In Exercises 3740, the graph of is given. Select the graph off.
 3.1.38: In Exercises 3740, the graph of is given. Select the graph off.
 3.1.39: In Exercises 3740, the graph of is given. Select the graph off.
 3.1.40: In Exercises 3740, the graph of is given. Select the graph off.
 3.1.41: The tangent line to the graph of at the point passes through the po...
 3.1.42: The tangent line to the graph of at the point passes through the po...
 3.1.43: In Exercises 43 46, sketch the graph of Explain how you found your ...
 3.1.44: In Exercises 43 46, sketch the graph of Explain how you found your ...
 3.1.45: In Exercises 43 46, sketch the graph of Explain how you found your ...
 3.1.46: In Exercises 43 46, sketch the graph of Explain how you found your ...
 3.1.47: Sketch a graph of a function whose derivative is always negative.
 3.1.48: Sketch a graph of a function whose derivative is always positive.
 3.1.49: In Exercises 4952, the limit represents for a function and a number...
 3.1.50: In Exercises 4952, the limit represents for a function and a number...
 3.1.51: In Exercises 4952, the limit represents for a function and a number...
 3.1.52: In Exercises 4952, the limit represents for a function and a number...
 3.1.53: In Exercises 53 55, identify a function that has the following char...
 3.1.54: In Exercises 53 55, identify a function that has the following char...
 3.1.55: In Exercises 53 55, identify a function that has the following char...
 3.1.56: Assume that Find if (a) is an odd function and (b) is an even function
 3.1.57: In Exercises 57 and 58, find equations of the two tangent lines to ...
 3.1.58: In Exercises 57 and 58, find equations of the two tangent lines to ...
 3.1.59: Graphical Reasoning The figure shows the graph of g (a) (b)(c) What...
 3.1.60: Graphical Reasoning Use a graphing utility to graph each function a...
 3.1.61: Graphical, Numerical, and Analytic Analysis In Exercises 61 and 62,...
 3.1.62: Graphical, Numerical, and Analytic Analysis In Exercises 61 and 62,...
 3.1.63: Graphical Reasoning In Exercises 63 and 64, use a graphing utility ...
 3.1.64: Graphical Reasoning In Exercises 63 and 64, use a graphing utility ...
 3.1.65: In Exercises 65 and 66, evaluate and and use the results to approxi...
 3.1.66: In Exercises 65 and 66, evaluate and and use the results to approxi...
 3.1.67: Graphical Reasoning In Exercises 67 and 68, use a graphing utility ...
 3.1.68: Graphical Reasoning In Exercises 67 and 68, use a graphing utility ...
 3.1.69: Writing In Exercises 69 and 70, consider the functions and where (a...
 3.1.70: Writing In Exercises 69 and 70, consider the functions and where (a...
 3.1.71: In Exercises 7180, use the alternative form of the derivative to fi...
 3.1.72: In Exercises 7180, use the alternative form of the derivative to fi...
 3.1.73: In Exercises 7180, use the alternative form of the derivative to fi...
 3.1.74: In Exercises 7180, use the alternative form of the derivative to fi...
 3.1.75: In Exercises 7180, use the alternative form of the derivative to fi...
 3.1.76: In Exercises 7180, use the alternative form of the derivative to fi...
 3.1.77: In Exercises 7180, use the alternative form of the derivative to fi...
 3.1.78: In Exercises 7180, use the alternative form of the derivative to fi...
 3.1.79: In Exercises 7180, use the alternative form of the derivative to fi...
 3.1.80: In Exercises 7180, use the alternative form of the derivative to fi...
 3.1.81: In Exercises 81 86, describe the values at which is differentiable.
 3.1.82: In Exercises 81 86, describe the values at which is differentiable.
 3.1.83: In Exercises 81 86, describe the values at which is differentiable.
 3.1.84: In Exercises 81 86, describe the values at which is differentiable.
 3.1.85: In Exercises 81 86, describe the values at which is differentiable.
 3.1.86: In Exercises 81 86, describe the values at which is differentiable.
 3.1.87: Graphical Analysis In Exercises 8790, use a graphing utility to fin...
 3.1.88: Graphical Analysis In Exercises 8790, use a graphing utility to fin...
 3.1.89: Graphical Analysis In Exercises 8790, use a graphing utility to fin...
 3.1.90: Graphical Analysis In Exercises 8790, use a graphing utility to fin...
 3.1.91: In Exercises 9194, find the derivatives from the left and from the ...
 3.1.92: In Exercises 9194, find the derivatives from the left and from the ...
 3.1.93: In Exercises 9194, find the derivatives from the left and from the ...
 3.1.94: In Exercises 9194, find the derivatives from the left and from the ...
 3.1.95: In Exercises 95 and 96, determine whether the function is different...
 3.1.96: In Exercises 95 and 96, determine whether the function is different...
 3.1.97: Graphical Reasoning A line with slope passes through the point and ...
 3.1.98: Conjecture Consider the functions and (a) Graph and on the same set...
 3.1.99: True or False? In Exercises 99102, determine whether the statement ...
 3.1.100: True or False? In Exercises 99102, determine whether the statement ...
 3.1.101: True or False? In Exercises 99102, determine whether the statement ...
 3.1.102: True or False? In Exercises 99102, determine whether the statement ...
 3.1.103: Let and Show that is continuous, but not differentiable, at Show th...
 3.1.104: Writing Use a graphing utility to graph the two functions and in th...
Solutions for Chapter 3.1: The Derivative and the Tangent Line Problem
Full solutions for Calculus: Early Transcendental Functions  4th Edition
ISBN: 9780618606245
Solutions for Chapter 3.1: The Derivative and the Tangent Line Problem
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4. Chapter 3.1: The Derivative and the Tangent Line Problem includes 104 full stepbystep solutions. Since 104 problems in chapter 3.1: The Derivative and the Tangent Line Problem have been answered, more than 45552 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245.

Absolute value of a real number
Denoted by a, represents the number a or the positive number a if a < 0.

Difference of two vectors
<u1, u2>  <v1, v2> = <u1  v1, u2  v2> or <u1, u2, u3>  <v1, v2, v3> = <u1  v1, u2  v2, u3  v3>

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

Distance (on a number line)
The distance between real numbers a and b, or a  b

Endpoint of an interval
A real number that represents one “end” of an interval.

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Exponential form
An equation written with exponents instead of logarithms.

Focal axis
The line through the focus and perpendicular to the directrix of a conic.

Frequency
Reciprocal of the period of a sinusoid.

Identity function
The function ƒ(x) = x.

Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + aekx, where a, b, c, and k are positive with b < 1. c is the limit to growth

Magnitude of a real number
See Absolute value of a real number

nset
A set of n objects.

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Shrink of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal shrink) by the constant 1/c or all of the ycoordinates (vertical shrink) by the constant c, 0 < c < 1.

Translation
See Horizontal translation, Vertical translation.

Vertical stretch or shrink
See Stretch, Shrink.

Ymin
The yvalue of the bottom of the viewing window.