Mathematics

Problem

Consider the function

p

defined by

p(x)= \begin{cases} x^{2}, & x\le 2,\\ 8x - x^{2}, & x>2. \end{cases}

Which of the following correctly describes all relative extrema of

p

(-\infty,\infty)

? a) A relative maximum at

x=2

and a relative minimum at

x=0

b) A relative maximum at

x=4

and a relative minimum at

x=0

c) A relative minimum at

x=0

only d) A relative maximum at

x=0

and a relative minimum at

x=4