Mathematics

Problem

Which statement best describes the role of the constant

C

in the antiderivative

y=F(x)+C

obtained from

\dfrac{dy}{dx}=f(x)

? a)

C

translates every antiderivative curve horizontally along the

x

–axis. b)

C

rescales the

x

–axis, determining the slope of any antiderivative curve. c)

C

shifts every antiderivative curve vertically, and its value is fixed by an initial condition. d)

C

changes the concavity of an antiderivative but not its position.