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# Solutions for Chapter 8.5: CRITICAL POINTS AND OPTIMIZATION ## Full solutions for Applied Calculus | 5th Edition

ISBN: 9781118174920 Solutions for Chapter 8.5: CRITICAL POINTS AND OPTIMIZATION

Solutions for Chapter 8.5
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##### ISBN: 9781118174920

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Applied Calculus, edition: 5. Applied Calculus was written by and is associated to the ISBN: 9781118174920. Since 21 problems in chapter 8.5: CRITICAL POINTS AND OPTIMIZATION have been answered, more than 33065 students have viewed full step-by-step solutions from this chapter. Chapter 8.5: CRITICAL POINTS AND OPTIMIZATION includes 21 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
• Definite integral

The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

• Directed line segment

See Arrow.

• Exponent

See nth power of a.

• Identity

An equation that is always true throughout its domain.

• Inferential statistics

Using the science of statistics to make inferences about the parameters in a population from a sample.

• Initial side of an angle

See Angle.

• Interquartile range

The difference between the third quartile and the first quartile.

• Linear programming problem

A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

• Polynomial in x

An expression that can be written in the form an x n + an-1x n-1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

• Principal nth root

If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.

• Real number line

A horizontal line that represents the set of real numbers.

• Sphere

A set of points in Cartesian space equally distant from a fixed point called the center.

• Standard deviation

A measure of how a data set is spread

• Standard form of a complex number

a + bi, where a and b are real numbers

• Sum of complex numbers

(a + bi) + (c + di) = (a + c) + (b + d)i

• Sum of two vectors

<u1, u2> + <v1, v2> = <u1 + v1, u2 + v2> <u1 + v1, u2 + v2, u3 + v3>

A graph in which (x, -y) is on the graph whenever (x, y) is; or a graph in which (r, -?) or (-r, ?, -?) is on the graph whenever (r, ?) is

• Tangent

The function y = tan x

• Translation

See Horizontal translation, Vertical translation.

• Vertex of a cone

See Right circular cone.

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