Define by . Choose the correct statement regarding the point…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

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