8th Edition

ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

Concept explainers

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

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Textbook Question

Chapter 10.2, Problem 27E

(a) Find the slope of the tangent line to the trochoid x = rθ − d sin θ, y = r − d cos θ in terms of θ. (See Exercise 10.1.40.)

(b) Show that if d < r, then the trochoid does not have a vertical tangent.

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Chapter 10.2, Problem 26E

Chapter 10.2, Problem 28E

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Chapter 10 Solutions

Calculus: Early Transcendentals

Ch. 10.1 - Sketch the curve by using the parametric equations...Ch. 10.1 - Sketch the curve by using the parametric equations...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

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(a) Find the slope of the tangent line to the trochoid x = rθ − d sin θ , y = r − d cos θ in terms of θ. (See Exercise 10.1.40.) (b) Show that if d &lt; r , then the trochoid does not have a vertical tangent.

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Chapter 10 Solutions

(a) Find the slope of the tangent line to the trochoid x = rθ − d sin θ , y = r − d cos θ in terms of θ. (See Exercise 10.1.40.) (b) Show that if d < r , then the trochoid does not have a vertical tangent.