Download Big Picture Day: Slopes of Tangent Lines and Derivative Techniques

Big Picture Day: Slopes of Tangent Lines and Derivative Techniques
This activity should help you understand the connections between graphs of a function, its
derivative, and the meaning of several things we have done in class. It will also help you see the
power behind the graphing calculator.
1) Put the following into y1 in your calculator: y = x3 –x2 –x – 2
Set “window” x: [-5, 4.4] scale = 1 and y: [-4.927,1.283] scale = 1 to see decimal values
later when we look at this in more detail. Sketch the graph below:
2) Sketch the derivative of the function:
3) Find the derivative of the function by using the definition for a derivative formula
Recall Pascal’s Triangle for help: {1 1 2 1 1 3 3 1 … } put this in y2 in the calculator
4) What are the 0’s of the derivative function?
Where on the graph of the original function do these occur?
Verify by calc then dy/dx
5) Verify that (-2,-12) is on the original graph by looking at a table of values.
Set table start to -2 and ∆Tbl = 1 (this yields whole numbers)
6) What does the column of the table represent for y2 based on any given value of x?
7) What is the slope of the line tangent to the curve at (-2,-12)? Verify by calc then dy/dx
8) What is the equation of the line tangent to the original curve at (-2,-12)?
9) Graph this line on the graphing calculator along with the other 2 graphs.