Graphically sketch the intuition behind the derivative.
State the formal definition of the derivative.
Compute the derivative of a function via the definition of the derivative.
Video2.1.1.Definition of the Derivative.
In this video we define the derivative at a point, translating a geometric problem about secant lines approaching a tangent line into a precise limit definition of the derivative.
Post-video reflection.
Try drawing your own sketch illustrating the definition of the derivative of a point.
Video2.1.2.Derivative of a function.
In this video we show how to extend from thinking about the derivative at a point to the derivative of a function. We apply this to the specific function \(f(x)=\frac{1}{x}\text{.}\)
Post-video reflection.
At the end we just “plugged in” h = 0 when evaluating the limit. Why didn’t we do that earlier?
Video2.1.3.Derivative of a Constant and x^2.
Let’s start applying the definition of the derivative to some of the simplest functions, like a constant function and the function \(f(x) = x^2\text{.}\)
Post-video reflection.
Try doing the same thing but for \(f(x) = x^3\text{.}\)
