Mathematics

Problem

Consider the piece-wise function

h(x)=\begin{cases} x+3, & x<0,\\ x^{2}+3, & x\ge 0. \end{cases}

Which statement correctly describes the nature of the point

x=0

for

h

? a)

h(0)

is a local minimum b)

h(0)

is both a local maximum and a local minimum c)

x=0

is neither a local maximum nor a local minimum d)

h(0)

is a local maximum