Consider a function defined parametrically: x = x(t), y = y(t). Suppose that we are interested in finding the points of extrema of this function. We can eliminate the parameter 't' to get y as a function of x. For example, consider
On elimination of f, we get y =
If we draw the graph of y = f(x) we can apply the basic definition of local maximum to claim that the function has a local maximum at x = 1.
FIGURE 5.233 ...