Mathematics

Problem

The function

f(x)=\begin{cases} x^{2}, & 0 \le x < 2,\\ 3, & x=2,\\ 4-x, & 2 < x \le 4 \end{cases}

is defined on

[0,4]

. Does

f

attain an absolute maximum on this interval? If so, state its value and where it occurs; if not, explain briefly why not.