Differentiation

Step 1: Differentiate the function.
The function is . To find the minimum, we need to take the derivative of the function and set it equal to zero. Using the product rule for differentiation:
Step 2: Set the derivative equal to zero.
To find critical points, we set :
Since is never zero, we have:
Step 3: Second derivative test.
To confirm that this is a minimum, we check the second derivative:
Substituting into the second derivative gives a positive value, confirming it is a minimum.
Step 4: Conclusion.
Thus, the function has a minimum at , which corresponds to option (C).