If f ′(x) = 3x2 + 2x – 5, find a possible function for f(x). Then find another possible function. Homework Help ✎
Undo the power rule.
The 3x² in f '(x) will become x³ in f(x). What will happen to the 2x and the −5?
The 2x in f '(x) will become x² in f(x).
The −5 in f '(x)will become −5x in f(x).
Giving us f(x) = x³ + x² − 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?