# What information about the function can be obtained from the tangent line?

• Generate a graph of this function, , years after 1974, using Excel or another graphing utility. (There are free downloadable programs like Graph 4.4.2 or Mathematics 4.0; or, there are also online utilities such as this site and many others.) Insert the graph into your Word document that contains all of your work details and answers. Be sure to label and number the axes appropriately. (Note: Some graphing utilities require that the independent variable must be âxâ instead of âtâ.)

1. Find the derivative of with respect to .

1. Choose a -value between 20 and 34. Calculate the value of

1. Interpret the meaning of the derivative value that you just calculated from part 3 in terms of the function.

1. If the function is reasonably accurate, for what value of will the rate of increase in MIPS per year reach 1,000,000 ? Approximately which year does that correspond to?

1. For the -value you chose in part 3 above, find the equation of the tangent line to the graph of at that value of . What information about the function can be obtained from the tangent line?