Develop an understanding of the derivative as an instantaneous rate of change, using geometrical, numerical, and analytical methods. Use this definition to find derivatives of algebraic and transcendental functions and combinations of these functions (using, for example, sums, composites, and inverses). Find second and higher order derivatives. Understand and use the relationship between differentiability and continuity. Understand and apply the Mean Value Theorem. Find derivatives of algebraic, trigonometric, logarithmic, and exponential functions. Find derivatives of sums, products, and quotients, and composite and inverse functions. Find derivatives of higher order, and use logarithmic differentiation and the Mean Value Theorem.
This learning video explores the mysterious physics behind boomerangs and other rapidly spinning objects. Students will get to make and throw their own boomerangs between video segments! A key idea presented is how torque causes the precession of angular momentum. One class period is required to complete this learning video, and the optimal prerequisites are a familiarity with forces, Newton's laws, vectors and time derivatives. Each student would need the following materials for boomerang construction: cardboard (roughly the size of a postcard), ruler, pencil/pen, scissors, protractor, and a stapler.