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

4-19.

For each

*f*(*x*), find its general antiderivative,*F*(*x*). Homework Help ✎*f*(*x*) = −2*f*(*x*) = −3*x*^{2}+ 6*x**f*(*x*) = 2(*x*+ 3)

Just as *f* '(*x*) is the slope function of *f*(*x*), *f*(*x*) is the slope function of *F*(*x*).

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*) = -2*x* + *C*

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

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

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