Maxima And Minima

Step 1: Find the derivative of
The first derivative of is:
Step 2: Set the derivative equal to zero to find critical points Factor out : Thus, is a critical point.
The quadratic has no real solutions.
Step 3: Analyze the function
Since the function is composed of even powers of , it has symmetry and no local maxima.
The only critical point is , and evaluating the second derivative at , we find that has a local minimum at this point.
Step 4: Conclusion
Thus, the function has only one minima.