needed help with this maths for econ question

2. Slughorn is teaching Malfoy how to make a magic potion which brings good luck. He tells Malfoy that, assuming all other ingredients are added correctly, the strength of the potion will initially increase as you add more and more Thyme, but too much of Thyme will make it a bad luck potion. In particular, assuming that the function f takes amount of Thyme (in milligrams) as domain and maps it to the amount of good luck. Then, f is given by: f($)=$2;if$53.7 :12m;ifm>3.7 Slughorn asks Malfoy to put in exactly 3.7 milligrams of Thyme in the potion. Is the function f con- tinuous in its domain (nonnegative real numbers)? If yes, prove it. If not, nd a point of discontinuity and prove that the function is not continuous at that point. In either case, use the formal denitions of continuity we have discussed in class and provide explanations for your answer. Note that for this particular function, if the function is continuous, then there is very little harm in adding an amount of Thyme which is very close the right amount but not exactly correct. On the other hand, if the function is not continuous, the difference in luck could be substantial. (8 points)