×

×

# Solutions for Chapter 3.1: The Derivative and the Tangent Line Problem

## Full solutions for Calculus: Early Transcendental Functions | 4th Edition

ISBN: 9780618606245

Solutions for Chapter 3.1: The Derivative and the Tangent Line Problem

Solutions for Chapter 3.1
4 5 0 370 Reviews
19
4
##### ISBN: 9780618606245

This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4. Chapter 3.1: The Derivative and the Tangent Line Problem includes 104 full step-by-step solutions. Since 104 problems in chapter 3.1: The Derivative and the Tangent Line Problem have been answered, more than 45552 students have viewed full step-by-step solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245.

Key Calculus Terms and definitions covered in this textbook
• Absolute value of a real number

Denoted by |a|, represents the number a or the positive number -a if a < 0.

• Difference of two vectors

<u1, u2> - <v1, v2> = <u1 - v1, u2 - v2> or <u1, u2, u3> - <v1, v2, v3> = <u1 - v1, u2 - v2, u3 - v3>

• Directrix of a parabola, ellipse, or hyperbola

A line used to determine the conic

• Distance (on a number line)

The distance between real numbers a and b, or |a - b|

• Endpoint of an interval

A real number that represents one “end” of an interval.

• equation of an ellipse

(x - h2) a2 + (y - k)2 b2 = 1 or (y - k)2 a2 + (x - h)2 b2 = 1

• Exponential form

An equation written with exponents instead of logarithms.

• Focal axis

The line through the focus and perpendicular to the directrix of a conic.

• Frequency

Reciprocal of the period of a sinusoid.

• Identity function

The function ƒ(x) = x.

• Logistic growth function

A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth

• Magnitude of a real number

See Absolute value of a real number

• n-set

A set of n objects.

• One-to-one rule of logarithms

x = y if and only if logb x = logb y.

• 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

• Pythagorean

Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

• Shrink of factor c

A transformation of a graph obtained by multiplying all the x-coordinates (horizontal shrink) by the constant 1/c or all of the y-coordinates (vertical shrink) by the constant c, 0 < c < 1.

• Translation

See Horizontal translation, Vertical translation.

• Vertical stretch or shrink

See Stretch, Shrink.

• Ymin

The y-value of the bottom of the viewing window.