F'(x) and f''(x)

Alright. I’m kinda stumped with this, and I could find a satisfactory answer elsewhere, so I’m hoping that perhaps someone else here knows.



Determine a function, f(x), such that f’(x) (the first derivative) is increasing when f’’(x) (the second derivative) is negative.



I know there’s no solution in the real number system, but there may be one in the complex. Eh. I wouldn’t know, really. :? So, if anyone can help I’d be eternally greatful.

i would doubt very much that there are any solutions to this problem. If you would examin the graphs of both f’(x) and f’’(x) you would know why. For any x^3 function, the f’(x) would either be a +ve parabola, or a -ve parabola depending the original function itself.



if you were to take f"(x) of f |–> x^3, you would notice that it is a straight line, this is the gradient difference of the f’(x).



In short, you need a function where the gradient change of f(x) is positive but the gradient change of f’(x) is negative, which contradicts itself. Therefore, there are no solutions to this problem.

Wow, I didn’t know such a thing was possible. Shows how much I paid attention in Diff Eq. Sorry.

i like maths!!

Bah. As I suspected. I was hoping there was perhaps something I had overlooked. Well, the question never specified the number system … the Erikian System has a nice ring to it… Alas! Thank you none the less.