Antiderivative Problem

[turophile]

Here's the problem:

Let f and g be functions such that f'''(x) = g'''(x) for all x, f''(0) = g''(0), f'(0) = g'(0), and f(0) = g(0). Show that f(x) = g(x) for all x.

I could use a hint to get started with this one.

 

[Deleted member 4993]

Here's the problem:

Let f and g be functions such that f'''(x) = g'''(x) for all x, f''(0) = g''(0), f'(0) = g'(0), and f(0) = g(0). Show that f(x) = g(x) for all x.

I could use a hint to get started with this one.

\(\displaystyle \int f'''(x) dx \ = \ \int g'''(x) dx \\)

\(\displaystyle f"(x) \ = \ g"(x) + C\)

since f"(0) = g"(0) ? C = 0. Then<

\(\displaystyle f''(x) \ = \ g"(x)\)

now continue.....