Differentiation in Real Functions: Solving for a Differentiable Function

[jetsetjoe]

Homework Statement

Show that there exists a differentiable real function:

(f(x))^5 + f(x) + x = 0

Homework Equations

??
definition of the derivative: lim (as x -> a) [f(x) - f(a)]/x-a

The Attempt at a Solution

Not really sure where to start with this one. any help would be appreciated.

 

[CompuChip]

By (f(x))^5, did you mean the fifth power f^5(x) = (f(x))^5[/tex] or the fifth derivative f^{(5)}(x) = \frac{d^5f(x)}{dx^5}. In the first case it&#039;s not a differential equation at all and I don&#039;t see why you need the definition for derivative. <br /> <br /> Please clarify what you mean exactly, and we&#039;ll give you a push in the right direction.