Power Functions Examples

There's a skill needed for integrals (we'll explain integrals later) that we'll consider now: thinking backwards. Instead of taking a function and figuring out its derivative, think about looking at a derivative and figuring out what sort of function it came from. Try this out when looking over solutions to derivatives.

If f ' (x) = 5x⁴, what could the original function f(x) be?

The derivative

f'(x) = 5x⁴ = 5x^5–1

looks like it came from the rule for derivatives of power functions. The original exponent must have been 5, therefore the original function could have been

f(x) = x⁵.