Calculus

Given the function , where , we want to find its minimum value. Step 1: Find the derivative of with respect to : Step 2: Set the derivative to zero to find critical points: Multiply both sides by : Step 3: Check the second derivative to confirm minimum: At , Since , is a point of local minimum. Step 4: Calculate the minimum value:

Let Step 1: Use the chain rule for differentiation: Step 2: Differentiate using the chain rule: where , so Therefore, Step 3: Combine the results: