 4.303: ?Explain why or why not Determine whether the following statements ...
 4.303: ?Locating extrema Consider the graph of a function f on the interva...
 4.303: ?Designer functions Sketch the graph of a continuous function that ...
 4.303: ?Designer functions Sketch the graph of a continuous function that ...
 4.303: ?Functions from derivatives Given the graphs of \(f^{\prime}\) and ...
 4.303: ?Critical points Find the critical points of the following function...
 4.7RE: ?Critical points Find the critical points of the following function...
 4.8RE: ?Critical points Find the critical points of the following function...
 4.10RE: ?Critical points Find the critical points of the following function...
 4.9RE: ?Critical points Find the critical points of the following function...
 4.11RE: ?Absolute values Consider the function f(x) = x  2 + x + 3 on ...
 4.12RE: ?Inflection points Does \(f(x)=2 x^{5}10 x^{4}+20 x^{3}+x+1\) have...
 4.13RE: ?Curve sketching Use the guidelines of this chapter to make a compl...
 4.14RE: ?Curve sketching Use the guidelines of this chapter to make a compl...
 4.15RE: ?Curve sketching Use the guidelines of this chapter to make a compl...
 4.16RE: ?Curve sketching Use the guidelines of this chapter to make a compl...
 4.17RE: ?Curve sketching Use the guidelines of this chapter to make a compl...
 4.18RE: ?Curve sketching Use the guidelines of this chapter to make a compl...
 4.19RE: ?Curve sketching Use the guidelines of this chapter to make a compl...
 4.20RE: ?Curve sketching Use the guidelines of this chapter to make a compl...
 4.21RE: ?Optimization A right triangle has legs of length h and r and a hyp...
 4.22RE: ?Rectangles beneath a curve A rectangle is constructed with one sid...
 4.23RE: ?Maximum length What two nonnegative real numbers a and b whose sum...
 4.24RE: ?Nearest point What point of the graph of \(f(x)=\frac{5}{2}x^{2}\...
 4.25RE: ?Mean Value Theorem The population of a culture of cells grows acco...
 4.26RE: ?Limits Evaluate the following limits. Use l'Hôpital's Rule when ne...
 4.27RE: ?Limits Evaluate the following limits. Use l'Hôpital's Rule when ne...
 4.28RE: ?Limits Evaluate the following limits. Use l'Hôpital's Rule when ne...
 4.29RE: ?Limits Evaluate the following limits. Use l'Hôpital's Rule when ne...
 4.30RE: ?Limits Evaluate the following limits. Use l'Hôpital's Rule when ne...
 4.31RE: ?Limits Evaluate the following limits. Use l'Hôpital's Rule when ne...
 4.32RE: ?Evaluate the following limits. Use l’ Hospital’s Rule when needed....
 4.33RE: ?Evaluate the following limits. Use l’ Hospital’s Rule when needed....
 4.34RE: ?Evaluate the following limits. Use l’ Hospital’s Rule when needed....
 4.35RE: ?Evaluate the following limits. Use l’ Hospital’s Rule when needed....
 4.36RE: ?\(1^{\infty},\ 0^0,\ \infty^0\) forms Evaluate the following limit...
 4.38RE: ?\(1^{\infty},\ 0^0,\ \infty^0\) forms Evaluate the following limit...
 4.39RE: ?\(1^{\infty},\ 0^0,\ \infty^0\) forms Evaluate the following limit...
 4.40RE: ?\(1^{\infty},\ 0^0,\ \infty^0\) forms Evaluate the following limit...
 4.41RE: ?\(1^{\infty},\ 0^0,\ \infty^0\) forms Evaluate the following limit...
 4.42RE: ?Determine which of the two functions grows faster, or state that t...
 4.43RE: ?Determine which of the two functions grows faster, or state that t...
 4.44RE: ?Determine which of the two functions grows faster, or state that t...
 4.45RE: ?Determine which of the two functions grows faster, or state that t...
 4.46RE: ?Determine which of the two functions grows faster, or state that t...
 4.47RE: ?Determine which of the two functions grows faster, or state that t...
 4.48RE: ?Determine which of the two functions grows faster, or state that t...
 4.49RE: ?Determine which of the two functions grows faster, or state that t...
 4.50RE: ?Determine the following indefinite integrals.\(\int\left(x^{8}3 x...
 4.51RE: ?Determine the following indefinite integrals.\(\int\left(\frac{1}{...
 4.52RE: ?Determine the following indefinite integrals.\(\int\frac{x^42\sqr...
 4.53RE: ?Determine the following indefinite integrals.\(\int(1+ \cos 3\thet...
 4.54RE: ?Determine the following indefinite integrals.\(\int2 \sec^2 x\ d x\)
 4.55RE: ?Determine the following indefinite integrals.\(\int\sec 2x \tan 2x...
 4.56RE: ?Determine the following indefinite integrals.\(\int2e^{2x} \ d x\)
 4.57RE: ?Determine the following indefinite integrals.\(\int\frac{12}{x} \ ...
 4.58RE: ?Determine the following indefinite integrals.\(\int\frac{dx}{\sqrt...
 4.59RE: ?Determine the following indefinite integrals.\(\int\frac{dx}{x^2+1...
 4.60RE: ?Determine the following indefinite integrals.\(\int\frac{1+ \tan \...
 4.61RE: ?Determine the following indefinite integrals.\(\int\left(\sqrt[4]{...
 4.62RE: ?Find the function with the following properties.\(f'(x)=3x^21\ an...
 4.63RE: ?Find the function with the following properties.f’(t) = sin t + 2t...
 4.64RE: ?Find the function with the following properties.\(g'(t)=t^2+t^{2}...
 4.65RE: ?Find the function with the following properties.\(h'(x)=sin^2\ x\ ...
 4.66RE: ?Two objects move along the xaxis with position functions \(x_1(t)...
 4.67RE: ?A rocket is launched vertically upward with an initial velocity of...
 4.68RE: ?Logs of logs Compare the growth rates of ln x, ln (ln x), and ln(l...
 4.70RE: ?Geometric mean Prove that \(\lim _{r \rightarrow 0}\ (\frac{a^r+b^...
 4.71RE: ?Evaluate the following limits in two different ways: Use the metho...
 4.72RE: ?Evaluate the following limits in two different ways: Use the metho...
 4.73RE: ?The functions \(f(x)=(x^x)^x\) and \(g(x)=x^{(x^{x})}\) are differ...
 4.74RE: ?Let n be a positive integer. Use graphical and/ or analytical meth...
 4.75RE: ?Consider the function \(g(x)=(1+1/x)^{x+a}\). Show that if \(0\ \l...
 4.76RE: ?A family of superexponential functions Let \(f(x)=(a+x)^x\), wher...
 4.68GP: GP A beach ball is thrown straight up, and some time later it lands...
 4.69PP: PP A Simple Solution for a Stuck Car If your car is stuck in the mu...
 4.70PP: A Simple Solution for a Stuck Car If your car is stuck in the mud a...
 4.71PP: A Simple Solution for a Stuck Car If your car is stuck in the mud a...
Solutions for Chapter 4: Maxima and Minima
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 4: Maxima and Minima
Get Full SolutionsSummary of Chapter 4: Maxima and Minima
With a working understanding of derivatives, we now undertake one of the fundamental tasks of calculus: analyzing the behavior of functions and producing accurate graphs of them.
Chapter 4: Maxima and Minima includes 78 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This expansive textbook survival guide covers the following chapters and their solutions. Since 78 problems in chapter 4: Maxima and Minima have been answered, more than 466981 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

Acute triangle
A triangle in which all angles measure less than 90°

Boxplot (or boxandwhisker plot)
A graph that displays a fivenumber summary

Branches
The two separate curves that make up a hyperbola

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Elements of a matrix
See Matrix element.

Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis

Inequality symbol or
<,>,<,>.

Leading term
See Polynomial function in x.

Line of symmetry
A line over which a graph is the mirror image of itself

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Nonsingular matrix
A square matrix with nonzero determinant

Onetoone rule of exponents
x = y if and only if bx = by.

Placebo
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.

Positive linear correlation
See Linear correlation.

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Right angle
A 90° angle.

Stem
The initial digit or digits of a number in a stemplot.

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.

Ymax
The yvalue of the top of the viewing window.