Let Determine whether is a point of local maximum

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f(x)=\begin{cases}x^{2}, & x\le 2,\\8x-12, & x>2.\end{cases}

Determine whether

x=2

is a point of local maximum, local minimum, or neither for

f

, and justify your answer.