Solved: For functions of one variable it is impossible for a continuous function to have
Chapter 9, Problem 21(choose chapter or problem)
For functions of one variable it is impossible for a continuous function to have two local maxima and no local minimum. But for functions of two variables such functions exist. Show that the function fsx, yd 2sx 2 2 1d 2 2 sx 2 y 2 x 2 1d 2 has only two critical points, but has local maxima at both of them. Then use a graphing device to produce a graph with a carefully chosen domain and viewpoint to see how this is possible.
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