Given the function $$ h(x) = x^3 - 3x^2 - 9x + 15 $$ . find ...

Question Analysis
This question evaluates the student's ability to find and classify the relative extrema of a polynomial function using the first derivative test.

Key Concept Explanation
The first derivative test is used to determine whether a critical point is a relative maximum, minimum, or neither by examining the sign changes of the first derivative around the critical point.

Step-by-step Solution
1. Find the first derivative: .
2. Set the first derivative equal to zero to find critical points: .
Factor: . So, and .
3. Use the first derivative test:
For ,

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Algebra-2

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