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“Find the critical values at which each of the following cubic functions is optimized and test...

“Find the critical values at which each of the following cubic functions is optimized and test the second-order conditions to see if the function is at a relative maximum, relative minimum, inflection point, or saddle point.

“(c) z = 8x^2 − 6y^3 + 144xy − 323
(d) z = 6x^3 + 6y^3 + 54xy − 195”

ans((c) (0, 0), inflection point; (648, −72), relative minimum
(d) (0, 0), inflection point; (−3, −3), relative maximum) show process

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