### Home > CALC > Chapter 4 > Lesson 4.3.1 > Problem 4-105

4-105.

A function has a derivative of

*f*′(*x*) = 6*x*^{2}+ 12*x*− 7. Homework Help ✎If

*f*(0) = 0, what was the original function?If

*f*(−2) = 25, what was the original function?Describe how you found the constant of integration in parts (a) and (b).

Solve for *C* by evaluating *f*(*x*) at *f*(0) = 0.

Note: you could also use the expression

*f*(*x*) = 2*x*³ + 6*x*² − 7*x* + *C*

Evaluate the given point to solve for *C*.

Note: you could also use the expression

Refer to hints in part (a) and (b).