Find all the maxima and minima of f ( x,y ) = x subject to the constraint g ( x,y ) = y^ 2 + x^ 4 − x^ 3 = 0
The lagrange multipliers dont give all the answers. What other method should i use?
2026-04-07 21:19:28.1775596768
Finding maxima and minima with another method than Lagrange multipliers
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Note that there is some $y$ such that $g(x,y) \ge 0$ iff $x^4 \le x^3$. Furthermore, $x^4 \le x^3 $ iff $x \in [0,1]$. Hence the problem becomes $\min \{ x | x \in [0,1] \}$ or the corresponding $\max$ problem.