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The document contains a mathematics competency test covering various topics. Here's an overview of the types of problems included:

1. **Function Analysis (Derivatives and Behavior)**: 
   - Questions involving increasing/decreasing intervals, extrema, and asymptotes of given functions. For instance:
     - **Question 1**: Asks for the interval where a function is decreasing.
     - **Question 2**: Requests the value of the minimum of a function.
     - **Question 6**: Identifying the vertical and horizontal asymptotes of a function's graph.
   
2. **Graph Interpretation and Optimization**:
   - **Question 4**: Focuses on finding the maximum value of a cubic function on a closed interval.
   - **Question 5**: Involves determining maximum and minimum points from the provided function's graph.

3. **Vector and Geometry Problems**:
   - **Question 9**: A vector problem involving a rectangular parallelepiped (rectangular box) and vector relationships.
   - **Question 11**: Vector problem in 3D space to find specific coordinates of a vector.
   - **Question 12**: Determines the projection of a point onto a plane in 3D space.

4. **Short Answer Geometry and Applied Math Problems**:
   - Problems dealing with maximizing the volume of geometric shapes, computing force in physics scenarios, and applying profit and production formulas in economics.
   - **Question 4 (Short Answer)**: Asks to find the dimensions of a box to maximize volume, where squares are cut from a square sheet.
   - **Question 5 (Short Answer)**: Involves maximizing profit given cost and revenue functions.

If you'd like, I can solve any specific problems from this test. Would you like help with any particular question or require further details? 

### 5 Possible Follow-up Questions:
1. How do you find the interval where a function is decreasing?
2. Can you explain how to find the maximum or minimum of a function from its derivative?
3. How do you compute the asymptotes of a rational function?
4. Can you solve the box problem in question 4 to find the optimal dimensions?
5. What is the method to calculate profit maximization in economics?

**Tip**: For function behavior problems, always start by finding the derivative to analyze increasing/decreasing intervals and critical points.

The document contains a mathematics competency test covering topics such as function analysis, vector geometry, graph interpretation, and applied mathematics.

This test covers mathematical topics including function analysis with derivatives, vector geometry problems, graph optimization, and applied math in physics and economics. Questions focus on key concepts such as maximizing profit and solving 3D vector equations.

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