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Sullivan 04 apcalc4e 45342 ch02 166 233 5pp August 7, 2023 12:54

UNIT 2 Differentiation: Definition and Fundamental Properties

C H A P T E R

2 The Derivative and

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Its Properties

2.1 Rates of Change
and the Derivative
2.2 The Derivative as a
Function;
Differentiability
2.3 The Derivative of a
Polynomial Function;
The Derivative of
x
y = e and y = ln x
2.4 Differentiating the
Product and the
Quotient of Two
Functions;
Higher-Order
Derivatives
Michael Collins, Apollo 11, NASA
2.5 The Derivative of the
Trigonometric The Apollo Lunar Module
Functions
“One Giant Leap for Mankind”
Chapter Project
On May 25, 1961, in a special address to Congress, U.S. president John F. Kennedy
Chapter Review proposed the goal “before this decade is out, of landing a man on the Moon and returning

AP Review Problems: him safely to the Earth.” Roughly eight years later, on July 16, 1969, a Saturn V rocket
R
launched from the Kennedy Space Center in Florida, carrying the Apollo 11 spacecraft and
Chapter 2
three astronauts—Neil Armstrong, Buzz Aldrin, and Michael Collins—bound for the Moon.
R
AP Cumulative Review
The Apollo spacecraft had three parts: the Command Module with a cabin for the
Problems: Chapters three astronauts; the Service Module that supported the Command Module with
1–2 propulsion, electrical power, oxygen, and water; and the Lunar Module for landing on the
Moon. After its launch, the spacecraft traveled for three days until it entered into lunar
orbit. Armstrong and Aldrin then moved into the Lunar Module, which they landed in the
flat expanse of the Sea of Tranquility. After more than 21 hours, the first humans to touch
the surface of the Moon crawled into the Lunar Module and lifted off to rejoin the
Command Module, which Collins had been piloting in lunar orbit. The three astronauts
then headed back to Earth, where they splashed down in the Pacific Ocean on July 24.
In 2022, NASA initiated the Artemis I program, designed to pave the way for the first
crewed Orion mission and eventually for the return of NASA astronauts to the surface of
the Moon and then on to Mars in the 2030s.
Explore some of the physics at work that allowed engineers and pilots to successfully maneuver the
Lunar Module to the Moon’s surface in the Chapter 2 Project on page 227.

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