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The question in the image is asking about the classification of critical points during the optimization of a function. Let's break it down.

In mathematical optimization, a **critical point** of a function is where the derivative (or gradient in multivariate functions) is zero or undefined. These points can be classified into various categories depending on the behavior of the function at those points.

Let's go through the options:

1. **Raiz da função, máximo global ou assíntota horizontal.**
   - This translates to "root of the function, global maximum, or horizontal asymptote." While a root is a critical point where the function crosses zero, horizontal asymptotes don't usually relate to critical points.

2. **Mínimo local, máximo global ou ponto de sela.**
   - This translates to "local minimum, global maximum, or saddle point." Critical points can often be classified into local minima, global maxima, or saddle points (where the function changes direction).

3. **Ponto de inflexão, assíntota vertical ou raiz da função.**
   - This translates to "inflection point, vertical asymptote, or root of the function." Inflection points are related to changes in concavity, but they do not necessarily occur at critical points unless the slope is zero.

4. **Mínimo global, máximo global ou ponto de sela.**
   - This is the same as option 2 but removes "local minimum." This option emphasizes only global behavior and saddle points.

5. **Mínimo local, máximo local ou ponto de inflexão.**
   - This translates to "local minimum, local maximum, or inflection point." Similar to option 2 but focuses only on local extrema and inflection points.

### Correct Option:
The most accurate classification of critical points during optimization involves **local minima, global maxima, or saddle points**, as these terms are common when discussing optimization in calculus. Thus, the correct answer seems to be:

**Option 2: Mínimo local, máximo global ou ponto de sela.**

Would you like any further clarifications or details? Here are five related questions to explore:

1. What is the difference between a local minimum and a global minimum?
2. How do saddle points differ from maxima and minima in multivariable functions?
3. What is the significance of second derivative tests in classifying critical points?
4. Can a critical point be neither a maximum, minimum, nor a saddle point?
5. How do we use gradient-based methods to find critical points in optimization?

**Tip**: Always check the first and second derivatives to classify critical points accurately!

Na otimização de uma função, o(s) ponto(s) crítico(s) encontrado(s) pode(m) ser classificado(s) em:

Descubra como classificar os pontos críticos em uma função otimizada, incluindo mínimos locais, máximos globais e pontos de sela. Explore testes de derivadas e conceitos de cálculo envolvidos na otimização de funções.

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