Calculus for Kinetic Modeling                                    Tangent Triangles and Tangent Intercept Functions
Name___________________________                                                                      Date___________

TIF Exercise 5 [total points = 5, required mastery level = 3.5]

[0.5 points] Compute tif(x) for the following function:

[1.5 points] Label the plot below with f(x) and tif(x), and construct a tangent triangle near x = 1.55, whose base is constructed from the point [0, tif(x)] to [x, tif(x)], and whose altitude is constructed from [x, tif(x)] to [x, f(x)].

[1.5 points] Directly compute the tangent slope function, tsf(x), using rise/run and the labels for the tangent triangle above (Note that the "rise" can be positive or negative).
 
 
 
 
 
 
 

[1 point] Using tsf(x) and tif(x), find the tangent line to f(x) at x = -1.2 and sketch it on the plot above.
 
 
 
 
 
 
 

[0.5 points] Using the geometrical relationship(s) between f(x) and tif(x), explain how you can tell which graph is f(x) and which is tif(x), using the "threading" concept. Why does this work?