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# Solutions for Chapter 4.1: USING FIRST AND SECOND DERIVATIVES ## Full solutions for Calculus: Single and Multivariable | 6th Edition

ISBN: 9780470888612 Solutions for Chapter 4.1: USING FIRST AND SECOND DERIVATIVES

Solutions for Chapter 4.1
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##### ISBN: 9780470888612

Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6. Chapter 4.1: USING FIRST AND SECOND DERIVATIVES includes 73 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 73 problems in chapter 4.1: USING FIRST AND SECOND DERIVATIVES have been answered, more than 23458 students have viewed full step-by-step solutions from this chapter.

Key Calculus Terms and definitions covered in this textbook
• Constant term

See Polynomial function

• Cotangent

The function y = cot x

• Differentiable at x = a

ƒ'(a) exists

• Direction angle of a vector

The angle that the vector makes with the positive x-axis

• Future value of an annuity

The net amount of money returned from an annuity.

• Graphical model

A visible representation of a numerical or algebraic model.

• Imaginary unit

The complex number.

• Inequality symbol or

<,>,<,>.

• Line of symmetry

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

• Linear regression line

The line for which the sum of the squares of the residuals is the smallest possible

• Multiplicative inverse of a complex number

The reciprocal of a + bi, or 1 a + bi = a a2 + b2- ba2 + b2 i

• Origin

The number zero on a number line, or the point where the x- and y-axes cross in the Cartesian coordinate system, or the point where the x-, y-, and z-axes cross in Cartesian three-dimensional space

• Polar coordinates

The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

• Polar distance formula

The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22 - 2r1r2 cos 1?1 - ?22

• Positive association

A relationship between two variables in which higher values of one variable are generally associated with higher values of the other variable, p. 717.

• Reciprocal function

The function ƒ(x) = 1x

• Reflection

Two points that are symmetric with respect to a lineor a point.

• Scientific notation

A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

• Slope

Ratio change in y/change in x

• Solution set of an inequality

The set of all solutions of an inequality

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