So the question states " If f satisfies |f(x)|</= |x|^(7/2) for all x, prove that f is differentiable at 0".

We just learned about Mean Value Theorem, Intermediate Value Theorem, Triangle inequality, Rolle's Theorem, and Extreme Value Theorem.

I don't even know where to start with this question. Any help would be greatly appreciated.

((I apologize in advance for the format that this is typed in, I am not that great at typing math stuff. (It is supposed to be less than or equal to; and it is the absolute value of x to the power of (7/2))).

Thank you for your time!