For the function , the critical point is found to be . Using the second derivative test, if , then is a relative minimum.
Answer & Analysis
Analysis
Question Analysis
This question assesses the student's ability to apply the second derivative test to determine the nature of a critical point. The function is given, and the critical point is provided. The student must evaluate the second derivative at the critical point to determine if it is a relative minimum.
Key Concept Explanation
The second derivative test states that if the second derivative at a critical point is greater than zero, then the function has a relative minimum at that point.
Step-by-step Solution
1. Given the function .
2. Find the first derivative: .
3. Set the first derivative equal to zero to find critical points: . Factor:
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