Part 7/7:
- The function values are ( f(0) = 1 ), ( f(2) = -3 ), ( f(-2) = 17 ), and ( f(4) = 17 ). Thus, the absolute minimum is (-3) at ( x=2) and the absolute maximum is (17) at both endpoints.
Conclusion
In summary, understanding local and absolute extrema, critical points, and how to apply the closed interval method is invaluable in calculus. These tools facilitate a more profound comprehension of the behaviors of functions, leading to significant insights in various mathematical applications. This foundational knowledge ultimately enhances one's mathematical skills and prepares one for more advanced topics in calculus.