 4.6.1: Sketch an arc where f and f have the sign combination ++. Do the sa...
 4.6.2: If the sign combination of f and f changes from ++ to + at x = c, t...
 4.6.3: The second derivative of the function f (x) = (x 4)1 is f (x) = 2(x...
 4.6.4: In Exercises 36, draw the graph of a function for which f and f tak...
 4.6.5: In Exercises 36, draw the graph of a function for which f and f tak...
 4.6.6: In Exercises 36, draw the graph of a function for which f and f tak...
 4.6.7: Sketch the graph of a function that could have the graphs of f and ...
 4.6.8: Sketch the graph of a function that could have the graphs of f and ...
 4.6.9: Sketch the graph of y = x2 5x + 4.
 4.6.10: Sketch the graph of y = 12 5x 2x2.
 4.6.11: Sketch the graph of f (x) = x3 3x2 + 2. Include the zeros of f , wh...
 4.6.12: Show that f (x) = x3 3x2 + 6x has a point of inflection but no loca...
 4.6.13: Extend the sketch of the graph of f (x) = cos x + 1 2 x in Example ...
 4.6.14: Sketch the graphs of y = x2/3 and y = x4/3.
 4.6.15: In Exercises 1536, find the transition points, intervals of increas...
 4.6.16: In Exercises 1536, find the transition points, intervals of increas...
 4.6.17: In Exercises 1536, find the transition points, intervals of increas...
 4.6.18: In Exercises 1536, find the transition points, intervals of increas...
 4.6.19: In Exercises 1536, find the transition points, intervals of increas...
 4.6.20: In Exercises 1536, find the transition points, intervals of increas...
 4.6.21: In Exercises 1536, find the transition points, intervals of increas...
 4.6.22: In Exercises 1536, find the transition points, intervals of increas...
 4.6.23: In Exercises 1536, find the transition points, intervals of increas...
 4.6.24: In Exercises 1536, find the transition points, intervals of increas...
 4.6.25: In Exercises 1536, find the transition points, intervals of increas...
 4.6.26: In Exercises 1536, find the transition points, intervals of increas...
 4.6.27: In Exercises 1536, find the transition points, intervals of increas...
 4.6.28: In Exercises 1536, find the transition points, intervals of increas...
 4.6.29: In Exercises 1536, find the transition points, intervals of increas...
 4.6.30: In Exercises 1536, find the transition points, intervals of increas...
 4.6.31: In Exercises 1536, find the transition points, intervals of increas...
 4.6.32: In Exercises 1536, find the transition points, intervals of increas...
 4.6.33: In Exercises 1536, find the transition points, intervals of increas...
 4.6.34: In Exercises 1536, find the transition points, intervals of increas...
 4.6.35: In Exercises 1536, find the transition points, intervals of increas...
 4.6.36: In Exercises 1536, find the transition points, intervals of increas...
 4.6.37: Sketch the graph of f (x) = 18(x 3)(x 1)2/3 using the formulas
 4.6.38: Sketch the graph of f (x) = x x2 + 1 using the formulas f (x) = 1 x...
 4.6.39: In Exercises 3942, sketch the graph of the function, indicating all...
 4.6.40: In Exercises 3942, sketch the graph of the function, indicating all...
 4.6.41: In Exercises 3942, sketch the graph of the function, indicating all...
 4.6.42: In Exercises 3942, sketch the graph of the function, indicating all...
 4.6.43: In Exercises 4348, sketch the graph over the given interval, with a...
 4.6.44: In Exercises 4348, sketch the graph over the given interval, with a...
 4.6.45: In Exercises 4348, sketch the graph over the given interval, with a...
 4.6.46: In Exercises 4348, sketch the graph over the given interval, with a...
 4.6.47: In Exercises 4348, sketch the graph over the given interval, with a...
 4.6.48: In Exercises 4348, sketch the graph over the given interval, with a...
 4.6.49: Are all sign transitions possible? Explain with a sketch why the tr...
 4.6.50: Suppose that f is twice differentiable satisfying (i) f (0) = 1, (i...
 4.6.51: Which of the graphs in Figure 20 cannot be the graph of a polynomia...
 4.6.52: Which curve in Figure 21 is the graph of f (x) = 2x4 1 1 + x4 ? Exp...
 4.6.53: Match the graphs in Figure 22 with the two functions y = 3x x2 1 an...
 4.6.54: Match the functions below with their graphs in Figure 23. (a) y = 1...
 4.6.55: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.56: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.57: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.58: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.59: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.60: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.61: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.62: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.63: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.64: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.65: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.66: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.67: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.68: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.69: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.70: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.71: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.72: In Exercises 5572, sketch the graph of the function. Indicate the t...
 4.6.73: In Exercises 7377, we explore functions whose graphs approach a non...
 4.6.74: In Exercises 7377, we explore functions whose graphs approach a non...
 4.6.75: In Exercises 7377, we explore functions whose graphs approach a non...
 4.6.76: In Exercises 7377, we explore functions whose graphs approach a non...
 4.6.77: In Exercises 7377, we explore functions whose graphs approach a non...
 4.6.78: Assume that f and f exist for all x and let c be a critical point o...
 4.6.79: Assume that f exists and f (x) > 0 for all x. Show that f (x) canno...
Solutions for Chapter 4.6: Graph Sketching and Asymptotes
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 4.6: Graph Sketching and Asymptotes
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. This expansive textbook survival guide covers the following chapters and their solutions. Since 79 problems in chapter 4.6: Graph Sketching and Asymptotes have been answered, more than 41898 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Chapter 4.6: Graph Sketching and Asymptotes includes 79 full stepbystep solutions.

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

Additive identity for the complex numbers
0 + 0i is the complex number zero

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

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

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>

Double inequality
A statement that describes a bounded interval, such as 3 ? x < 5

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

Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1  z1) 1x  i z 22 Á 1x  z n where the z1 are the zeros of ƒ

Linear regression
A procedure for finding the straight line that is the best fit for the data

Nautical mile
Length of 1 minute of arc along the Earth’s equator.

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Quotient rule of logarithms
logb a R S b = logb R  logb S, R > 0, S > 0

Radian measure
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

Real number line
A horizontal line that represents the set of real numbers.

Semimajor axis
The distance from the center to a vertex of an ellipse.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Solve a triangle
To find one or more unknown sides or angles of a triangle

Solve by substitution
Method for solving systems of linear equations.

yintercept
A point that lies on both the graph and the yaxis.