Find a formula for a constant function using the mean value theorem

[lamictal]

Homework Statement

Let x ϵ R such that f'(x) = 3x^2. Prove that f(x) = x^3 + c for some c ϵ R using the Mean Value Theorem.

Homework Equations

The Attempt at a Solution

I used two functions f(x) and g(x) that have the same derivative namely f'(x). Applying the theorem I am able to work up until f(x) = g(x), I am unsure of where to go from there.

 

[ystael]

If you reached the conclusion $$f(x) = g(x)$$ from only the hypothesis $$f'(x) = g'(x)$$, something is clearly wrong, since that deduction is false.

You have a function that's expected to be a constant, namely $$f(x) - x^3$$. Work with that.