Calculus for Kinetic Modeling                                    Tangent Triangles and Tangent Intercept Functions
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TIF Exercise 2 [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 = -0.6, 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.
 
 
 
 
 
 
 

[1 point] Using tsf(x) and tif(x), find the tangent line to f(x) at x = 0.45 and sketch it on the plot above.
 
 
 
 
 
 
 

[0.5 points] How do we justify using rise/run (above) to compute tsf(0), since there is no tangent triangle at the origin (it degenerates to a point)?