A function is defined piecewise on the closed interval with finitely many pieces

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

Problem

A function

f

is defined piecewise on the closed interval

[a,b]

with finitely many pieces. When determining the absolute extrema of

f

[a,b]

, which set of

x

-values must always be examined? (a) The endpoints

x=a

and

x=b

, every interior point where

f'(x)=0

, and every junction point where the pieces meet (b) Only the endpoints

x=a

and

x=b

x=a

and

x=b

, and every interior point where

f'(x)=0

(d) Only the interior points of each piece where

f'(x)=0