I'm pretty sure you can't do $f''(x^3)=f((x^3)^2)$. To Clarify I DO NOT mean $(f(x^3))''$ but $f''(x^3)$
Asked
Active
Viewed 75 times
3
-
for all x or for some x? – djechlin Nov 22 '15 at 05:51
-
question didn't really specify. I assume it's for all x then. – Richard Chang Nov 22 '15 at 05:52
-
Are there no other known properties of the function, like perhaps that it's a polynomial (in which case the solution would be trivial but I'm brainstorming). – Addem Nov 22 '15 at 06:08
-
Original question: Given that f'(x)=g(x) and g'(x)=f(x^2), what is f''(x^3). – Richard Chang Nov 22 '15 at 06:15
1 Answers
2
It's just $f(x^6)$. Other than that, you can't really tell much.
-
-
It is just substitution. As you correctly noted $f''(x^3)$ is different to $(f(x^3))''$. – Ian Miller Nov 22 '15 at 06:01
-
I kind of need a function to visualize what's going on. Is there a function where that situation is true? – Richard Chang Nov 22 '15 at 06:04
-
-
The original question was just: Give that f'(x)=g(x) and g'(x)=f(x^2), what is f''(x^3). To be honest, I think they messed up the notation. – Richard Chang Nov 22 '15 at 06:09
-
1If $f''(x) = f(x^2)$ then these two things are the same function. Therefore if I do something to the first function, and to the second function, the results must also be the same. So if I substitute $x^3$ into both, the results should be the same for both. so $f''(x^3)=f((x^2)^3) = f(x^6)$. – Addem Nov 22 '15 at 06:16
-
This might sound stupid but I just want to make sure that my reasoning is correct. So because x could be any value, whether we plug in x^6 or any number it will be true. So therefore if we plug in x^3 it should still work since the "x" values are the same on both sides. – Richard Chang Nov 22 '15 at 06:44