Let t be the 7th digit of your Student ID. Consider the set S = [--10, 10] and answer each of the following questions:
(a) [8 MARKS] Define the function g on S:
G (x):= { -| x-t| if x e[-10,t)
1- e(x-t) if x E[t,10]
Plot this function in a graph and explain formally whether g is continuous on S.
(b) [6 MARKS] Does g have a maximum and minimum on the set S? Prove or disprove
(c) [10 MARKS] Find the global maxima and minima of g on the set S if they exist.
(d) [6 MARKS] Argue informally whether the sufficient conditions for maxima are sat- isfied.