 4.1.1: (a) A function f is increasing on (a, b) if whenevera<x1 < x2 < b.(...
 4.1.2: Let f(x) = 0.1(x3 3x2 9x). Thenf(x) = 0.1(3x2 6x 9) = 0.3(x + 1)(x ...
 4.1.3: Suppose that f(x) has derivative f(x) = (x 4)2ex/2.Then f (x) = 12 ...
 4.1.4: . Consider the statement The rise in the cost of living sloweddurin...
 4.1.5: Use the graph of y = f (x) in the accompanying figureto determine t...
 4.1.6: Use the graph of y = f(x) in the accompanying figureto replace the ...
 4.1.7: In each part, use the graph of y = f(x) in the accompanyingfigure t...
 4.1.8: Use the graph in Exercise 7 to make a table that shows thesigns of ...
 4.1.9: 910 A sign chart is presented for the first and second derivativeso...
 4.1.10: 910 A sign chart is presented for the first and second derivativeso...
 4.1.11: 1114 TrueFalse Assume that f is differentiable everywhere. Determin...
 4.1.12: 1114 TrueFalse Assume that f is differentiable everywhere. Determin...
 4.1.13: 1114 TrueFalse Assume that f is differentiable everywhere. Determin...
 4.1.14: 1114 TrueFalse Assume that f is differentiable everywhere. Determin...
 4.1.15: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.16: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.17: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.18: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.19: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.20: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.21: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.22: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.23: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.24: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.25: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.26: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.27: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.28: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.29: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.30: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.31: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.32: 1532 Find: (a) the intervals on which f is increasing, (b) the inte...
 4.1.33: 3338 Analyze the trigonometric function f over the specified interv...
 4.1.34: 3338 Analyze the trigonometric function f over the specified interv...
 4.1.35: 3338 Analyze the trigonometric function f over the specified interv...
 4.1.36: 3338 Analyze the trigonometric function f over the specified interv...
 4.1.37: 3338 Analyze the trigonometric function f over the specified interv...
 4.1.38: 3338 Analyze the trigonometric function f over the specified interv...
 4.1.39: In parts (a)(c), sketch a continuous curve y = f(x)with the stated ...
 4.1.40: In each part sketch a continuous curve y = f(x) withthe stated prop...
 4.1.41: 4146 If f is increasing on an interval [0, b), then it followsfrom ...
 4.1.42: 4146 If f is increasing on an interval [0, b), then it followsfrom ...
 4.1.43: 4146 If f is increasing on an interval [0, b), then it followsfrom ...
 4.1.44: 4146 If f is increasing on an interval [0, b), then it followsfrom ...
 4.1.45: 4146 If f is increasing on an interval [0, b), then it followsfrom ...
 4.1.46: 4146 If f is increasing on an interval [0, b), then it followsfrom ...
 4.1.47: 4748 Use a graphing utility to generate the graphs of f andf over t...
 4.1.48: 4748 Use a graphing utility to generate the graphs of f andf over t...
 4.1.49: 4950 Use a CAS to find f and to approximate the xcoordinatesof the ...
 4.1.50: 4950 Use a CAS to find f and to approximate the xcoordinatesof the ...
 4.1.51: Use Definition 4.1.1 to prove that f(x) = x2 is increasing on [0, +).
 4.1.52: Use Definition 4.1.1 to prove that f x = 1 / x is decreasing on (0 ...
 4.1.53: 5354 Determine whether the statements are true or false.If a statem...
 4.1.54: 5354 Determine whether the statements are true or false.If a statem...
 4.1.55: In each part, find functions f and g that are increasing on(, +) an...
 4.1.56: In each part, find functions f and g that are positiveand increasin...
 4.1.57: (a) Prove that a general cubic polynomialf(x) = ax3 + bx2 + cx + d ...
 4.1.58: From Exercise 57, the polynomial f(x) = x3 + bx2 + 1 hasone inflect...
 4.1.59: Use Definition 4.1.1 to prove:(a) If f is increasing on the interva...
 4.1.60: Use part (a) of Exercise 59 to show that f(x) = x + sin xis increas...
 4.1.61: Use part (b) of Exercise 59 to show that f(x) = cos x xis decreasin...
 4.1.62: Let y = 1/(1 + x2). Find the values of x for which y isincreasing m...
 4.1.63: 6366 Suppose that water is flowing at a constant rate intothe conta...
 4.1.64: 6366 Suppose that water is flowing at a constant rate intothe conta...
 4.1.65: 6366 Suppose that water is flowing at a constant rate intothe conta...
 4.1.66: 6366 Suppose that water is flowing at a constant rate intothe conta...
 4.1.67: Suppose that a population y grows according to the logisticmodel gi...
 4.1.68: Suppose that the number of individuals at time t in a certainwildli...
 4.1.69: Suppose that the spread of a flu virus on a college campusis modele...
 4.1.70: The logistic growth model given in Formula (1) is equivalenttoyekt ...
 4.1.71: Assuming that A,k, and L are positive constants, verify thatthe gra...
 4.1.72: Writing An approaching storm causes the air temperatureto fall. Mak...
 4.1.73: Writing Explain what the sign analyses of f(x) and f (x)tell us abo...
Solutions for Chapter 4.1: ANALYSIS OF FUNCTIONS I: INCREASE, DECREASE, AND CONCAVITY
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 4.1: ANALYSIS OF FUNCTIONS I: INCREASE, DECREASE, AND CONCAVITY
Get Full SolutionsCalculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Since 73 problems in chapter 4.1: ANALYSIS OF FUNCTIONS I: INCREASE, DECREASE, AND CONCAVITY have been answered, more than 42153 students have viewed full stepbystep solutions from this chapter. Chapter 4.1: ANALYSIS OF FUNCTIONS I: INCREASE, DECREASE, AND CONCAVITY includes 73 full stepbystep solutions. This 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.

Amplitude
See Sinusoid.

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

Central angle
An angle whose vertex is the center of a circle

Cotangent
The function y = cot x

Difference of functions
(ƒ  g)(x) = ƒ(x)  g(x)

Equation
A statement of equality between two expressions.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial

Mode of a data set
The category or number that occurs most frequently in the set.

Numerical model
A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

Origin
The number zero on a number line, or the point where the x and yaxes cross in the Cartesian coordinate system, or the point where the x, y, and zaxes cross in Cartesian threedimensional space

Parallel lines
Two lines that are both vertical or have equal slopes.

Perihelion
The closest point to the Sun in a planet’s orbit.

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

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Zero of a function
A value in the domain of a function that makes the function value zero.