Graph Of Derivative, Part 1

As you slide "A" along the function f(x), the green dot traces out the graph of the derivative function, f ' (x); that is, the function whose height represents the slope of f(x).

1. Notice the relationship between f(x) and f ' (x). When f (x) is decreasing, what is true about f ' (x)? Where do the roots of f ' (x) occur? What feature of f (x) corresponds to a DECREASING derivative?

2. Now, slide "k" up and down and displace f(x) by different amounts. What happens to the graph of the derivative function? (You've seen this before!)

Dave Matthews, Created with GeoGebra