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

4-19.

For each function below, write the equation of its general antiderivative, $F$.

Just as $f '\left(x\right)$ is the slope function of $f\left(x\right)$, $f\left(x\right)$ is the slope function of $F\left(x\right)$.

1. $f\left(x\right) = –2$

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

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

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

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

3. $f\left(x\right) = –3x^{2} + 6x$

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

4. $f\left(x\right) = 2\left(x + 3\right)$

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