#### Answer

a) The extreme value theorem
b) The closed interval method

#### Work Step by Step

a) If f is continuous on a closed interval [a, b], then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some number c and d in [a, b]
b) First, find the critical number by using f'(c)=0, then, compare them, the largest one is the abs. max., the smallest one is the abs. min.