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(3): Hmmmm by TomM)
"While the appeal of "calculus without calculus" is what made you think of the problem in the first place, it is not intrinsic to the problem itself. It works not because you found the derivative of x², but because you exploited a property of the graph of that specific function. "
as i have said, the problem is formulated in terms of gradient NOT derivative. i chose the language deliberately to make the similarity clear, since this is how i solved it then, starting from "calculus without
calculus". it is precisely part of the problem to realise that the gradient
of x^2 is the tangent. so youre saying "remove half the problem
because its too hard"
obviously i am wrong thinking its easy, considering that after
having solved most of it (TomM) still no one has answered
it..
re(4): Hmmmm
