Math 124 Worksheet for Week 3 Graphs of f x and f x In this worksheet you ll practice getting information about a derivative from the graph of a function and vice versa At the end you ll match some graphs of functions to graphs of their derivatives If f r is a function then remember that we define f x h f x h f x lim A 10 Week 3 If this limit exists then f z is the slope of the tangent line to the graph off at the point I f x Consider the graph of f x below UNSERE 1 Use the graph to answer the following questions a Are there any values for which the derivative f x does not exist b Are there any values z for which f x 0 Worksheet Math 124 Week 3 c This particular function f has an interval on which its derivative f r is constant What is this interval What does the derivative function look like there Estimate the slope of f r on that interval d On which interval or intervals is f x positive e On which interval or intervals is f r negative Again sketch a graph of the derivative on those intervals f Now use all your answers to the questions to sketch a graph of the derivative function f z on the coordinate plane below