To try to clarify what we're doing, let's take a fairly simple example:
(Original post by KyraBloke)
Maximum point on a graph is where it turns. As you approach this point, the gradient gets smaller and smaller - i.e reaches 0. Hence why you set it equal to 0. If you set it equal to 1, then at that point, the gradient would be 1, which is larger than 0, hence the gradient there would be bigger than at 0.
Stationary points of y=f(x) are where dy/dx=0. However, if we are looking for the maximum gradient, then we want to take dy/dx as our original function, let's call this g(x):
The maxima and minima of the gradient of f(x) are then found where g'(x)=f''(x)=0, i.e: where sin(x)=0. With reference to the graph of sin(x), this makes sense.
Last edited by james.h; 09-06-2012 at 23:11.