### Home > CALC > Chapter 4 > Lesson 4.1.2 > Problem4-19

4-19.

For each $f(x)$, find its general antiderivative, $F(x)$.

Just as $f^\prime(x)$ is the slope function of $f(x)$, $f(x)$ is the slope function of $F(x)$.

1. $f(x) =-2$

If the slope function, $f(x)$, is horizontal, then the original function, $F(x)$, is _______________.

If $f(x)$ is horizontal, then $F(x)$ will be linear: $F(x) = -2x + C$

1. $f ( x ) = \frac { 3 } { 2 } x ^ { - 1 / 2 }$

Check your work by finding the derivative of $F(x)$. Are your $+$ and $−$ signs correct?

1. f(x) = −3x2 + 6x

For all of these, don't forget the $+C$.

1. f(x) = 2(x + 3)

If the slope function, $f(x)$, is linear, then the original function, $F(x)$, will be _____________________________.