Mathematics

Problem

The function

s

is given by

s(x)=\begin{cases} (x-2)^{2}+1,& x<2,\\ -x+5,& 2\le x<4,\\ (x-4)^{2}+3,& x\ge 4. \end{cases}

Classify the nature of

s

at each break point

x=2

and

x=4

(state “relative maximum”, “relative minimum”, or “neither” for each).