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): Err.... by friedlinguini)
True, but seeing as we are asked to prove a gradient of a curve for all values of x, we are going to have to consider the actual gradient at some point. You can hide an explanation by calling the gradient the 'flooble' if you want, but at the end of the day the question asks us to consider gradients - besides, the initial definition uses the world 'gradient' in the first place. You are going to have to assume some property of gradients at some point to prove the final equation to be true...
re(5): Err....
