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My teacher gave me a very complicated explanation on how to solve an optimization problem so I just wanted clarification. To do so I have laid out what I think is the simplest way to solve it.

  1. Take the derivative of the function given.
  2. take $f'(0)$ of the derivative to get the critical number.
  3. Plug in both the critical number to original function and also plug in the extreme values (i.e. if it gives you a control of $[-5,5]$ or $0<x<200$).

And from those answers you can see your max and min?

Demosthene
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alex
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1 Answers1

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See some ideas below, keep in mind that there are many techniques to solve optimization problems.

Case 1: Unconstrained optimization problem:

  1. Derivative of the function $f'(x)$
  2. Compute $f''(x)$ to check is your objective function is semidefinite or definite.
  3. If your problem is convex then solve $f'(x)=0$ and substitute in the objective function, since your stationary point will be the optimal solution.

Case 2: Constrained optimization problem:

The common procedures are establish the Karush-Kuhn-Tucker conditions or compute the lagrangian to solve your problem as an unconstrained problem.

guille_NP
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