In this exercise you are asked to experiment with finding an interval small enough around a given point so that the function appears to have a locally constant rate of change.

If you are confused by the following instructions, please watch the instructional video at the end of Section 4.4.

Step 1: Download Exercise 4.4.4and open it in GC.

Step 2: Zoom in (shift-click-drag) enough times around the point (x0,g(x0)) until you are convinced that the displayed part of the graph has a rate of change that is essentially constant over that interval. At some point during this zooming process, you will start to see two horizontal purple arrows.

Step 3: Changethe set value of dx with an appropriate value, to have GC calculate the constant rate of change over the visible x-interval from Step 2.Entering this new value of dxwill also make GC graph the linear function having that rate of change that passes through (x0,g(x0)). Set the value of dx to make the purple arrows appear within your graph window.

Note that the graph of a function whose rate of change exists at any moment is a nice smooth, continuous curve with no cusps and with no vertical tangent lines.

What is the value of dxyou chose? (If Step 2 was impossible, type DNE) ____________

As you zoomed in you eventually see two purple arrows. What mathematical idea does one arrow represent?

• secant line
• constant rate of change
• moment
• quantity
• dx
• tangent line
• dy
• linear graph
• slope

What is the value of mthat GC calculates based on the dxvalue you picked? (Note that, as you make dx smaller, dx=0.001,0.0001,0.00001 etc, the rate of change m never becomes essential constant. If Step 2 was impossible, type DNE) ______________

Exercise 4.4.4

\fExpr X_0, X_1