DISCUSS - DISCOVER: Minimizing a Distance When we seek a minimum or maximum value of a function, it is some- times easier to work with a simpler function instead. (a) Suppose g(x) = VF(x) where f(x) = 0 for all x. Explain why the local minima and maxima of f and g occur at the same values of x. (b) Let g(x) be the distance between the point (3, 0) and the point (x, x*) on the graph of the parabola y = x'. Express g as a function of x. (c) Find the minimum value of the function g that you found in part (b). Use the principle described in part (a) to sim- plify your work.

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