For a function that is continuous on an open interval

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

Problem

For a function

f

that is continuous on an open interval

I

, let

F

and

G

satisfy

F'(x)=G'(x)=f(x)

for all

x

I

. Which of the following must be true on the interval

I

? (a)

\dfrac{F(x)}{G(x)}

is constant (b)

F(x)-G(x) \text{ varies linearly with } x

(c)

F(x)-G(x)

is constant (d)

F(x)\,G(x)

is constant