g(x) = equation to tangent line of f(x) at point (a,f(a)) Line B = Secant line approximating the instantaneous slope at point (a,f(a). The slope of the secant line provides an approximation of the slope of the tangent line (instantaneous slope). Slider A= Slide to change the point of tangency and where the secant line is centered at. Slider H= Slide to change the distance from a to the points the secant line crosses. (f(x+h)-f(x-h))/(2h) Right Click to zoom in and out
What do you notice about the Secant Line as you change H? What happens when you increase H? What happens when you decrease H? How does the secant line relate to the tangent line? What do you notice happens to the tangent line as a approaches negative infinity? What do you notice happens to the tangent line as A approaches positive infinity? What happens in terms of slope of the tangent line?