A continuous function is defined by f(x)= cases 4, & 1 x 3, -3, & 3< x 6, 2, & 6< x 7

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

Problem

A continuous function

f

is defined by

f(x)=\begin{cases}4, & 1\le x\le 3,\\-3, & 3< x\le 6,\\2, & 6< x\le 7.\end{cases}

Let

F

satisfy

F'(x)=f(x)

and

F(1)=5

. What is

F(7)

? (a) 4 (b) 1 (c) 6 (d) 9