T turophile Junior Member Joined May 22, 2010 Messages 94 Jul 25, 2010 #1 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.
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.
D Deleted member 4993 Guest Jul 25, 2010 #2 turophile said: 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. Click to expand... \(\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.....
turophile said: 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. Click to expand... \(\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.....
