(a) Let f be a continuous function of one variable. Show that if f has two local maxima, then f must also have a local minimum.
(b) The analogue of part (a) does not necessarily hold for continuous functions of more than one variable, as we now see. Consider the function
f (x,y) = 2 − (xy2 − y − 1)2 − (y2 − 1)2.
Show that f has just two critical points—and that both of them are local maxima.
(c) Use a computer to graph the function f in part (b).
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