That's Calculus!

Episode 4 and 5: Josh and the Mathemagician
Running times: 43 and 38 minutes

In Part 1, Josh meets a mysterious woman dressed as a bag lady who can find where any function has its largest and smallest values. He undertakes a quest to find the secret to her arcane knowledge of max and min. In Part 2, Josh advances his status in the mysterious cult by learning to compute the derivatives of various and complicated functions. His brave efforts earn his induction into the cult.
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Mathematical Content: Part 1 covers the definition of the derivative. Josh begins with the formula for the slope of a line, derives the (limit) definition of the derivative, and uses this definition to find the derivatives of the functions x squared, and then x to any (positive integer) power. Part 2 covers some rules for computing derivatives, including a proof of the product rule, and examples for use of the sum, product and chain rules.