Below are the post on differential calculus, derivatives, and their applications. Scroll down or use these links to take you directly to the various sections:
DEFINITION OF THE DERIVATIVE
Local Linearity 1 (8-29-2012) The graphical manifestation of differentiability with pathological examples.
Local Linearity 2 (8-31-2012) Using local linearity to approximate the tangent line. A calculator exploration.
Discovering the Derivative (8-18-2015) A graphing calculator exploration
The Derivative 1 (9-5-2012) Definition of the derivative
The Derivative 2 (9-7-2012) Calculators and difference quotients
Difference Quotients 1 (9-10-2012)
Difference Quotients II (9-12-2012)
Tangents and Slopes (9-1-2015)
Why Radians? (12-12-2012) Don’t do calculus without them
The Derivative Rules 1 (9-14-2012) Constants, sums and differences, powers.
The Derivative Rules 2 (9-17-2012) The Product rule
The Derivative Rules 3 (9-19-2012) The Quotient rule
Experimenting with CAS – Chain Rule (7-3-2013) Discovering the Chain Rule
Power Rule Implies the Chain Rule (9-20-2014)
Foreshadowing the Chain Rule (9-20-2013)
The Chain Rule (9-21-2012)
Derivative Practice – Numbers (10-202012) Derivative from tables of numbers
Derivative Practice – Graphs (10-3-2012) Derivative from graphs
The Calculus of Inverses (11-12-2012) Derivatives of the Inverse Trigonometry functions
Implicit Differentiation (9-28-2017) Where to start this topic.
Inverses Graphically and Numerically (11-14-2012) Derivatives of inverses – the hard way and the easy way.
Implicit Differentiation of Parametric Equations (5-17-2014) BC topic.
A Vector’s Derivatives (1-14-2015) What they mean and how to find them. BC topic.
Units (1-26-2018) The units of derivatives and integrals
APPLICATIONS: THE MEAN VALUE THEOREM (MVT)
Fermat’s Penultimate Theorem (9-24-2012) Extreme values occur where the derivative is 0 or undefined (critical points)
Rolle’s Theorem (9-26-2012)
The Mean Value Theorem I (9-28-2012) Proof
The Mean Value Theorem II (10-1-2012) Graphical Considerations
Mean Numbers (9-25-2013) Using the MVT
Mean Tables (9-16-2014) A discussion of 2003 AB 90 in which students which short table of values could be those for a function describes in the stem. Mean Value Theorem, Graph analysis
Darboux’s Theorem (8-18-2014) Derivatives obey the Intermediate Value Theorem
What’s a Mean Old Average Anyway? (4-29-2014) Helping students understand the difference between the average rate of change of a function, the average value of a function, and the Mean Value theorem
APPLICATIONS: GRAPHING AND EXTREME VALUES
Concepts Related to Graphs (10-15-2012)
The Shapes of a Graph (10-17-2012) There are only 5
Joining the Pieces of a Graph (10-19-2012)
Extreme Values (10-22-2012)
Curves with Extrema? (10-19-2015)
Reading the Derivative’s Graph (10-26-2012) My all time most read post.
Using the Derivative to Graph the Function (9-9-2015)
Real “Real Life” Graph Reading (10-29-2012)
Far Out! (10-31-2012) Finding the important points on very strange problems (CAS recommended but not necessary. By hand you’ll get some great Algebra practice) From the Good Question series.
Soda Cans (5-13-2015) Why the best can isn’t. Links to good videos.
Extremes without Calculus (10-13-2014) A student’s question. From the Good Question series
OTHER APPLICATIONS OF DERIVATIVES
Determining the Indeterminate (9-24-2015)
Determining the Indeterminate (12-6-2015) Same name, different post. Examining an implicit relation
Locally Linear L’Hôpital (5-31-2013) Demonstrating L’Hôpital’s Rule (a/k/a L’Hospital’s Rule)
L’Hôpital’s Rules the Graph (6-5-2013)
Related Rate Problems I (10-8-2012) Introduction: problems without geometry
Type 2 Questions: Linear Motion (3-9-2013)
Type 3 Questions: Graph Analysis (3—13-2013)
Type 5: Table Questions (3-20-2018)
Type 7 Questions: Miscellaneous (3-27-2018) Related rate, implicit differentiation, etc.
Type 8: Parametric and Vector Questions (3-30-2018) BC topics