CPM Homework Help : CALC Problem 3-93

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

Hint 1:

Undo the power rule.

Hint 2:

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

Hint 3:

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

Answer:

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.

Hint 4:

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