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

3-93.

If $f^\prime(x) = 3x^2 + 2x − 5$, write a possible equation for $f$. Then write another possible function. Homework Help ✎

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?