# Differential Calculus

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:

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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)

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FINDING DERIVATIVES

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)

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

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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

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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)

Concavity (10-24-2012)

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.

Open or Closed? (11-2-2012) Include the endpoints or not? See also Going Up?

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

A Standard Problem (5-14-2013) A max/min problem a further look at the same problem The Marble and the Vase (10-23-2014).From the Good Question series.

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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

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REVIEW NOTES

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