Define the function by f(x)= cases x^ 2 , & x1

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Define the function

f

f(x)= \begin{cases} x^{2}, & x<0,\\ 3, & x=0,\\ |x|, & 0<x<1,\\ 0, & x=1,\\ \sin(\pi x), & x>1. \end{cases}

Let

g(x)=\displaystyle\int_{-2}^{x} f(t)\,dt

. For which of the following values of

x

must

g'(x)

fail to exist? (a)

x=0 \text{ and } x=1

(b)

x=1

only (c)

x=0

only (d)

g'(x)

\text{ exists for all real } x