Please help with calculus question!

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Determine the location of any maxima, minima, or saddle points for: (tell what each one is)


Jul 22nd, 2015

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Let f be a function with two variables with continuous second order partial derivatives fxx, fyy and fxy at a critical point (a,b). Let

D = fxx(a,b) fyy(a,b) - fxy2(a,b)
  1. If D > 0 and fxx(a,b) > 0, then f has a relative minimum at (a,b).
  2. If D > 0 and fxx(a,b) < 0, then f has a relative maximum at (a,b).
  3. If D < 0, then f has a saddle point at (a,b).
  4. If D = 0, then no conclusion can be drawn.

We now present several examples with detailed solutions on how to locate relative minima, maxima and saddle points of functions of two variables. When too many critical points are found, the use of a table is very convenient.




y=9 or 2

minima= (5, 2)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 22nd, 2015

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