(a) Let f be a continuous function of one variable. Show that if f has two local maxima

Chapter 4, Problem 53

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(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 (x y2 y 1)2 (y2 1)2 . Show that f has just two critical pointsand that both of them are local maxima. T (c) Use a computer to graph the function f in part (b).

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