Extrema of Functions of Two Variables (Unconstrained) f=x^6+y^6+6/(xy)

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This video explains how to determine the critical points as well as the relative extrema or saddle points of a function of two variables.
  1. Mathispower4u
  2. relative
  3. extrema
  4. maximum
  5. minimum
  6. critical
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I'm confused on the partial fxx=30x^4+12/x^3y and on the last slide fxx=6/x^y^2 which one is right. Im missing something. Help

saltybird