Calculus for Kinetic Modeling                                    Tangent Triangles and Tangent Intercept Functions
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TIF Exercise 4 [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 = 0.725, 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 = -0.75 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), even in a complicated situation as above.