Consider the function f(x)= cases x^ 2 +1, & x 1, |x-1|+2, & x>1

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

Problem

Consider the function

f(x)=\begin{cases} x^{2}+1, & x\le 1,\\ |x-1|+2, & x>1. \end{cases}

At which value(s) of

x

does

f

attain a local minimum? (a) At

x=0

and

x=1

(b) Only at

x=0

x=1

(d) The function has no local minimum