In this lesson, we learn how to approximate the derivative of a function by making the interval h smaller and smaller. The derivative describes the rate of change of the function at a given point and is represented by the slope of the tangent line to the function at that point. With the help of an applet, we can see how the slope of the secant line changes as we move the interval closer to the point of interest, eventually obtaining an approximation of the slope of the tangent line, which is the derivative.
Be able to explain the definition of the derivative (THE fundamental notion of Calculus) in terms of a limit of the difference quotient and more importantly the Cartesian plot of secant lines vs tangent line to a function.
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