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What commands should I use in Mathematica to obtain the maximum or minimum of a function subject to conditions?

For example, find the maximum of the following function?

$\qquad T=\sqrt[3]{2\,x+5} + \sqrt[3]{2\,y+5} , x > 0 ,y > 0 , x + y=3$

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closed as off-topic by corey979, m_goldberg, Carl Lange, MarcoB, Daniel Lichtblau Jan 29 at 16:17

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  • $\begingroup$ Maximize -- just search for it in the docs. $\endgroup$ – Michael E2 Jan 28 at 19:50
  • $\begingroup$ BTW, people here generally like users to post code as Mathematica code instead of just images or TeX, so they can copy-paste it. It makes it convenient for them and more likely you will get someone to help you. You may find this this meta Q&A helpful $\endgroup$ – Michael E2 Jan 28 at 19:51
  • $\begingroup$ Edited ... .... $\endgroup$ – Walter Jan 28 at 20:05
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For the maximum

Maximize[
  {Power[2 x + 5, (3)^-1] + Power[2 y + 5, (3)^-1], x > 0, y > 0, x + y == 3},
  {x, y}]

{4, {x -> 3/2, y -> 3/2}}

For the minimum, Mathematica says there no minimum on the line x + y == 3 that is a minimum with the open set of the search space.

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  • $\begingroup$ ,thanks, it is not clear to me the use of Power in replacement of the cubic roots of each expression, please clarify $\endgroup$ – Walter Jan 28 at 21:09
  • $\begingroup$ I get it. Thank You $\endgroup$ – Walter Jan 29 at 2:01

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