Lesson 3.1
Slopes
of Curves and Derivatives
|
What this
lesson is about
This lesson introduces the
most fundamental idea of the course: the derivative.
As you work through the lesson, you will learn how to
- find the slope of a curve
at a given point on it
- define the derivative
of a function at a point
- use the definition to
calculate derivatives.
This lesson should take
P - Q hours to complete.
Begin
the lesson
From the
textbook (Section
2.7, page 151)
- The text discusses derivatives
from a slightly different viewpoint from the course notes, using tangent lines
as motivation (we look at tangent lines in the next lesson).
- Note the alternate form
of the derivative definition in box 2 - this is another useful way of thinking
about derivatives.
- Example 1 works out the
derivative of another simple function.
- For more practice with
the definition of the derivative once you've worked through the lesson, the
following problems at the end of the section are recommended: numbers 3, 11,
13, 15, 17, 19, 21.
From the
Starter Library
The following notebook may
be helpful: in the Calculus-Derivatives/Derivatives section,
- Derivative via Definition
Links on
the slopes of curves and derivatives
- The
Linear Nature of Graphs.
- From UBC: slope of a
curve by zooming.
- 23-3
The Derivative (using h)
- Calculating a derivative
from first principles, using the slope of a tangent line as motivation (we
do tangent lines in Lesson 3.2). Has a MV/LM notebook at the end.
- Limit
Definition of the Derivative - HMC Calculus Tutorial
- Calculating the derivative
from first principles. Uses the slope of the tangent line as motivation.
- Lesson
40--The Derivative; Slope of a Curve
- A series of pages with
exercises about finding the derivative froim the definition (slope motivated).
- Calculus:
Derivatives part 1
- Derivatives as slopes
of curves. Has an animated zoom.
- Karl's
Calculus Tutor - 4.0 Derivatives: Trials of the Animals
- Motivation for derivatives
as slopes.
- Karl's
Calculus Tutor - 4.1 Derivatives: The Main Pillar
- More on the definition
of the derivative, with slope and rates of change as motivation.
- Geometric
Interpretation of the Derivative
- A tutorial, based on
slopes. Uses calculations with a graphing calculator. Has quizzes, review,
etc.
- Derivatives:
Graphical/Learn
- More on zooming. Has
worksheets for various mathematical software packages.
- Visual
Calculus - Definition of derivative - 8
- A tutorial on the definition
of a derivative at a point. Uses Java or IBM pro Techexplorer.
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