1. **Stating the problem:** You want to solve a variation table where you have 3 given values but one value is missing. 2. **Understanding variation tables:** Variation tables show how a function changes over intervals, often including values of the function and its derivative or rate of change. 3. **Key formula:** If the function is increasing or decreasing, the missing value can be found using the concept of linear interpolation or the mean value theorem, depending on the context. 4. **Step-by-step approach:** - Identify the known values and their positions in the table. - Use the relationship between the values (e.g., if the function is linear between points, use the formula for linear interpolation: $$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$$ where $y$ is the missing value at $x$). - If the function is not linear, use the derivative or rate of change information to estimate the missing value. 5. **Example:** Suppose you know $f(a)$, $f(b)$, and $f'(a)$ but $f(c)$ is missing. You can approximate $f(c)$ by: $$f(c) \approx f(a) + f'(a)(c - a)$$ 6. **Summary:** Use the known values and the function's behavior (increasing/decreasing, derivative) to set up an equation and solve for the missing value. This method helps you fill in missing data in variation tables logically and accurately.