Define:
d/dx(f(x)) = f'(x)
where f'(x) = gradient (or slope) of f(x) at x = x.
Prove that:
d/dx(x^2) = 2x
without using calculus.
(In reply to
re(4): Hmmmm by Cheradenine)
I don't think TomM is asking you to make the problem any easier, just clearer. Solving the problem is difficult enough without the added puzzle of trying to figure out what you're asking. I'm curious why you think mentioning a tangential line is fully half the problem. Most math students who haven't taken calculus are only familiar with slopes as they apply to lines anyway. Mentioning the tangential line I think only makes it easier for someone to know what the problem is asking. I don't see how it makes it any easier to solve, though.
I think some of us are abstaining because anybody who has taken a single calculus course knows how to bridge the gap.
Incidentally, I'd recommend ditching the d/dx notation, as well as "at x = x" (which is a tautology). You can simply say "Define f(x) = x². Define f'(x) as the slope of the curve generated by f(x) for any given value of x. Prove that f'(x) = 2x."
re(5): Hmmmm
