Mathematics

Problem

Define

f

f(x)=\begin{cases}-(x-2)+3,&x\le 2\\(x-2)^{2}+3,&x>2\end{cases}

. Choose the correct statement regarding the point

x=2

. a)

x=2

is a point of local maximum of

f

. b)

x=2

is not a critical point of

f

. c)

x=2

is a point of local minimum of

f

. d)

x=2

is a point of inflection of

f