Consider the function defined by p(x)= cases x^ 2 , & x 2, 8x - x^ 2 , & x>2

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider the function

p

defined by

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

Which of the following correctly describes all relative extrema of

p

(-\infty,\infty)

? (a) A relative maximum at

x=2

and a relative minimum at

x=0

(b) A relative maximum at

x=4

and a relative minimum at

x=0

x=0

only (d) A relative maximum at

x=0

and a relative minimum at

x=4