### Home > CALC > Chapter 3 > Lesson 3.3.1 > Problem3-93

3-93.

If $f^\prime(x) = 3x^2 + 2x – 5$, find a possible function for $f(x)$. Then find another possible function.

Undo the power rule.

The $3x^²$ in $f^\prime(x)$ will become $x^³$ in $f(x)$. What will happen to the $2x$ and the $-5$?

The $2x$ in $f^\prime(x)$ will become $x^²$ in $f(x)$.

The $-5$ in $f^\prime(x)$ will become $-5x$ in $f(x)$.
Giving us $f(x) = x^³ + x^² − 5x$. But there are other functions that also have the same derivative.

To find another $f(x)$, think about the Power Rule. What happens to a constant when you differentiate?