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: Hmmmm by TomM)
Personally, I'd get rid of all calculus terminology altogether. Even the appearence of calculus operators will throw people who haven't seen them before ("Why can't I just cancel the d's?").
If we're going back to first principles, I'd propose couching the problems in framework in which calculus was originally invented: physics. For example, "An object's position at any time t is given by the function f(t) = t². Prove that the object's velocity is given by the function f'(t) = 2t, without using any calculus operators." That at least poses the problem in terms most people will understand.
re(2): Hmmmm
