Lab 3 – Tangent Lines and Linear Approximation



1. The tangent line of \( y = f(x) \) at \( x = a \) is a linear approximation of the function \( f(x) \) near \( x = a \); that is, it is the “line” that you see when you zoom in on the graph of \( y = f(x) \) at \( x = a \). The SageMath app below plots \( y = f(x) \) together with the line with a given slope through the point \( (a, f(a)) \). You can change the slope of this line and the zoom level. For the functions and corresponding values of \( a \) given in your lab report, use the app below to zoom in on the function at \( x = a \) until it looks like a line. Then, adjust the slope of the line until it coincides with the graph of \( y = f(x) \). Record the slope in your lab report. For parts (c) and (d), attach printouts of the function and its (approximate) tangent line at zoom level 1.


Name:
Skip to toolbar