To determine whether a function has a minimum or maximum value, and to find that value, we generally follow these steps:

### 1. **Differentiate the function**:
   Take the first derivative of the function to find the points where the slope of the curve is zero (critical points).

### 2. **Set the derivative equal to zero**:
   Solve for \( x \) where the derivative is zero. These are the potential minimum or maximum points.

### 3. **Second Derivative Test**:
   - Take the second derivative of the function.
   - Evaluate the second derivative at the critical points:
     - If \( f''(x) > 0 \), the point is a **minimum**.
     - If \( f''(x) < 0 \), the point is a **maximum**.
     - If \( f''(x) = 0 \), the test is inconclusive, and other methods like the **First Derivative Test** or analyzing the function's behavior around the critical points are needed.

Would you like to apply this process to a specific function or scenario? If you provide one, I can walk you through the steps.

Here are 5 example questions related to finding minimum or maximum values:

1. What is the maximum value of \( f(x) = x^2 - 4x + 3 \)?
2. How do you find the minimum of \( f(x) = -2x^2 + 8x - 5 \)?
3. Can a function have both a minimum and maximum value?
4. What is the significance of the second derivative in determining concavity?
5. How can you tell if a critical point is a saddle point?

**Tip**: When using the second derivative test, always check for concavity to ensure whether you are dealing with a maximum or a minimum.

Learn how to find maximum and minimum values of functions using derivatives with step-by-step solutions. This page covers critical points, first and second derivative tests, and is suitable for students in Grades 10-12.

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