5. (3 pts) Let f(x) = = 3 tan(x/2) + 2x + 1. Using the Sage Math cell in Exercise 5 of the
online version of the lab, define f(x). Then, define a new function m(b), where b ≠ -0.5,
such that m(b) is the slope of the line through the points (-0.5, f(-0.5)) and (6, f(6)).
(a) For each value of b listed in the table below, use your function m(b) to determine the
slope of the line that passes through the points (-0.5, f(-0.5)) and (b, f(6)). Record
the slopes you found in the table below.
Value of b
Slope m
Value of b
Slope m
1
-0.53676
-0.33391
-0.4978
(b) Using your function m(b) with b = -0.4993, define a new function g(x) which gives
the line through the points (-0.5, f(-0.5)) and (-0.4993, f(-0.4993)). Plot both
f(x) and g(x) together on the interval (-2,2). When you are finished, print your
code and output and attach the printout to your lab report.