 4.2.1: A function f has a relative maximum at x0 if there is an openinterv...
 4.2.2: Suppose that f is defined everywhere and x = 2, 3, 5, 7 arecritical...
 4.2.3: Suppose that f is defined everywhere and x = 2 andx = 1 are critica...
 4.2.4: Let f(x) = (x2 4)2. Then f(x) = 4x(x2 4) andf (x) = 4(3x2 4). Ident...
 4.2.5: (a) Show that both of the functions f(x) = (x 1)4 andg(x) = x3 3x2 ...
 4.2.6: (a) Show that f(x) = 1 x5 and g(x) = 3x4 8x3 bothhave stationary po...
 4.2.7: 714 Locate the critical points and identify which critical points a...
 4.2.8: 714 Locate the critical points and identify which critical points a...
 4.2.9: 714 Locate the critical points and identify which critical points a...
 4.2.10: 714 Locate the critical points and identify which critical points a...
 4.2.11: 714 Locate the critical points and identify which critical points a...
 4.2.12: 714 Locate the critical points and identify which critical points a...
 4.2.13: 714 Locate the critical points and identify which critical points a...
 4.2.14: 714 Locate the critical points and identify which critical points a...
 4.2.15: 1518 TrueFalse Assume that f is continuous everywhere. Determine wh...
 4.2.16: 1518 TrueFalse Assume that f is continuous everywhere. Determine wh...
 4.2.17: 1518 TrueFalse Assume that f is continuous everywhere. Determine wh...
 4.2.18: 1518 TrueFalse Assume that f is continuous everywhere. Determine wh...
 4.2.19: 1920 The graph of a function f(x) is given. Sketch graphs of y = f ...
 4.2.20: 1920 The graph of a function f(x) is given. Sketch graphs of y = f ...
 4.2.21: 2124 Use the graph of f shown in the figure to estimate all values ...
 4.2.22: 2124 Use the graph of f shown in the figure to estimate all values ...
 4.2.23: 2124 Use the graph of f shown in the figure to estimate all values ...
 4.2.24: 2124 Use the graph of f shown in the figure to estimate all values ...
 4.2.25: 2532 Use the given derivative to find all critical points of f ,and...
 4.2.26: 2532 Use the given derivative to find all critical points of f ,and...
 4.2.27: 2532 Use the given derivative to find all critical points of f ,and...
 4.2.28: 2532 Use the given derivative to find all critical points of f ,and...
 4.2.29: 2532 Use the given derivative to find all critical points of f ,and...
 4.2.30: 2532 Use the given derivative to find all critical points of f ,and...
 4.2.31: 2532 Use the given derivative to find all critical points of f ,and...
 4.2.32: 2532 Use the given derivative to find all critical points of f ,and...
 4.2.33: 3336 Find the relative extrema using both first and second derivati...
 4.2.34: 3336 Find the relative extrema using both first and second derivati...
 4.2.35: 3336 Find the relative extrema using both first and second derivati...
 4.2.36: 3336 Find the relative extrema using both first and second derivati...
 4.2.37: 3750 Use any method to find the relative extrema of the function f ...
 4.2.38: 3750 Use any method to find the relative extrema of the function f ...
 4.2.39: 3750 Use any method to find the relative extrema of the function f ...
 4.2.40: 3750 Use any method to find the relative extrema of the function f ...
 4.2.41: 3750 Use any method to find the relative extrema of the function f ...
 4.2.42: 3750 Use any method to find the relative extrema of the function f ...
 4.2.43: 3750 Use any method to find the relative extrema of the function f ...
 4.2.44: 3750 Use any method to find the relative extrema of the function f ...
 4.2.45: 3750 Use any method to find the relative extrema of the function f ...
 4.2.46: 3750 Use any method to find the relative extrema of the function f ...
 4.2.47: 3750 Use any method to find the relative extrema of the function f ...
 4.2.48: 3750 Use any method to find the relative extrema of the function f ...
 4.2.49: 3750 Use any method to find the relative extrema of the function f ...
 4.2.50: 3750 Use any method to find the relative extrema of the function f ...
 4.2.51: 5160 Give a graph of the polynomial and label the coordinatesof the...
 4.2.52: 5160 Give a graph of the polynomial and label the coordinatesof the...
 4.2.53: 5160 Give a graph of the polynomial and label the coordinatesof the...
 4.2.54: 5160 Give a graph of the polynomial and label the coordinatesof the...
 4.2.55: 5160 Give a graph of the polynomial and label the coordinatesof the...
 4.2.56: 5160 Give a graph of the polynomial and label the coordinatesof the...
 4.2.57: 5160 Give a graph of the polynomial and label the coordinatesof the...
 4.2.58: 5160 Give a graph of the polynomial and label the coordinatesof the...
 4.2.59: 5160 Give a graph of the polynomial and label the coordinatesof the...
 4.2.60: 5160 Give a graph of the polynomial and label the coordinatesof the...
 4.2.61: In each part: (i) Make a conjecture about the behavior of thegraph ...
 4.2.62: Sketch the graph of y = (x a)m(x b)n for the statedvalues of m and ...
 4.2.63: 6366 Find the relative extrema in the interval 0 <x< 2,and confirm ...
 4.2.64: 6366 Find the relative extrema in the interval 0 <x< 2,and confirm ...
 4.2.65: 6366 Find the relative extrema in the interval 0 <x< 2,and confirm ...
 4.2.66: 6366 Find the relative extrema in the interval 0 <x< 2,and confirm ...
 4.2.67: 6770 Use a graphing utility to make a conjecture about the relative...
 4.2.68: 6770 Use a graphing utility to make a conjecture about the relative...
 4.2.69: 6770 Use a graphing utility to make a conjecture about the relative...
 4.2.70: 6770 Use a graphing utility to make a conjecture about the relative...
 4.2.71: 7172 Use a graphing utility to generate the graphs of f andf over t...
 4.2.72: 7172 Use a graphing utility to generate the graphs of f andf over t...
 4.2.73: 7376 Use a CAS to graph f and f , and then use those graphsto estim...
 4.2.74: 7376 Use a CAS to graph f and f , and then use those graphsto estim...
 4.2.75: 7376 Use a CAS to graph f and f , and then use those graphsto estim...
 4.2.76: 7376 Use a CAS to graph f and f , and then use those graphsto estim...
 4.2.77: In each part, find k so that f has a relative extremum at thepoint ...
 4.2.78: (a) Use a CAS to graph the functionf(x) = x4 + 1x2 + 1and use the g...
 4.2.79: Functions similar tof(x) = 12ex2/2arise in a wide variety of statis...
 4.2.80: Functions of the formf(x) = xnexn! , x> 0where n is a positive inte...
 4.2.81: Let h and g have relative maxima at x0. Prove or disprove:(a) h + g...
 4.2.82: Sketch some curves that show that the three parts of thefirst deriv...
 4.2.83: Writing Discuss the relative advantages or disadvantagesof using th...
 4.2.84: Writing If p(x) is a polynomial, discuss the usefulnessof knowing z...
Solutions for Chapter 4.2: ANALYSIS OF FUNCTIONS II: RELATIVE EXTREMA; GRAPHING POLYNOMIALS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 4.2: ANALYSIS OF FUNCTIONS II: RELATIVE EXTREMA; GRAPHING POLYNOMIALS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Since 84 problems in chapter 4.2: ANALYSIS OF FUNCTIONS II: RELATIVE EXTREMA; GRAPHING POLYNOMIALS have been answered, more than 38364 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Chapter 4.2: ANALYSIS OF FUNCTIONS II: RELATIVE EXTREMA; GRAPHING POLYNOMIALS includes 84 full stepbystep solutions.

Arccotangent function
See Inverse cotangent function.

Arcsecant function
See Inverse secant function.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Control
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable

Equation
A statement of equality between two expressions.

Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).

Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a  ƒ(x) = q.

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

Logistic regression
A procedure for fitting a logistic curve to a set of data

Main diagonal
The diagonal from the top left to the bottom right of a square matrix

Modified boxplot
A boxplot with the outliers removed.

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

Normal curve
The graph of ƒ(x) = ex2/2

Pie chart
See Circle graph.

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

Root of an equation
A solution.

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Xmin
The xvalue of the left side of the viewing window,.