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
Standard solution by friedlinguini)
your solution is the definition of derivative, since
it involves finding the gradient in the limit as
deltax tends to 0. however its not really
what i had in mind, since this is calculus
(f'(x) = f(x+dx) - f(x) / dx, as dx tends to 0)
a solution is possible without taking this limit.
consider that youve already established that
the gradient is a tangent. also note the definition
of tangent for circles. in a circle a tangent
only intersects the curve once. because of
y = x^2 shape, this is also true, the tangent
will only touch the curve once.
use the fact that the tangent only touches the curve once to obtain a non calculus solution.
re: Standard solution
