Mathematics

Problem

The function

g

is defined by

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

Which statement best describes the relative (local) extrema of

g

? a)

g

has a relative maximum at

x=1

and a relative minimum at

x=3

. b)

g

has neither a relative maximum nor a relative minimum at

x=1

x=3

. c)

g

has a relative maximum at

x=1

only. d)

g

has a relative minimum at

x=1

and a relative maximum at

x=3