The problem statement asks you to **find the absolute minimum of \( f \) on the interval \([-11, 6]\)**. However, **the function \( f \) is not provided** in the image. ### **Step-by-Step Solution Template** To solve such a problem, here's what you would normally do: 1. **Find the endpoints of the interval**: \( x = -11 \) and \( x = 6 \). 2. **Find the critical points** of \( f \) in the open interval \((-11, 6)\) by solving \( f'(x) = 0 \). 3. **Evaluate \( f \) at the endpoints and at the critical points**. 4. **Compare all values**: The smallest value is the **absolute minimum**. ### **What You Need** You must know the explicit formula for \( f(x) \). --- #### **Example (Assume \( f(x) = x^2 \))** 1. **Endpoints**: \( f(-11) = 121 \), \( f(6) = 36 \) 2. **Critical Point**: \( f'(x) = 2x = 0 \implies x = 0 \) 3. \( f(0) = 0 \) 4. **Compare**: \( f(-11) = 121 \), \( f(6) = 36 \), \( f(0) = 0 \) **Absolute minimum is at \( x = 0 \), and \( f(0) = 0 \).** --- ### **Final Answer Format** > The absolute minimum of \( f \) is \( f(\boxed{\ }) = \boxed{\ } \). --- **Please provide the function \( f(x) \) so I can give you the exact step-by-step solution and final answer!**