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# scan0087 - AMS 261 Mid-Term II Problem I(20 pts Suppose...

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Unformatted text preview: AMS 261 Mid-Term II Problem I (20 pts. ) Suppose that you want to ﬁnd the maximum and minimum values of f(x, y) = x2 + 3y2 subject to the constraint x + y = 2. a.) Sketch the constraint equation and a few contours of f b.) On your sketch, show the location (approximately of course) of all the maxima and minima of f subject to the constraint, how many are there. c.) Use the method of Langrange multipliers to ﬁnd the exact location(s) of the extrema that you found in part (b). d) Are the point(s) you found in (c ) maxima or minima? E , 3/ \ a (3‘ kajg 1‘ "IX a K J Mime no «a ' \ Consider the integral I I f (x, y)dydx l 3 a.) Sketch the region over which the integral is being performed b.) Rewrite the integral with the integration being performed in the opposite order .m’, ...
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