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Example 2: Find the relative maxima and minima of the function f (x) = x 3 - 6x 2 +9x + 15. using the second derivative test. Solution: The given function is f (x) = x 3 - 6x 2 +9x + 15. f' (x) = 3x 2

A minimum or a maximum is called an extreme point. A local extreme point is the smallest or largest value in its neighborhood. If it is also the smallest or largest at the entire domain of the function, it is called a global

We look for a function that works. Suppose that $f'(x)=(x-2)(x-5)$. Then $f'(x)$ is positive for $x\lt 2$, negative strictly between $2$ and $5$, and positive for $x\gt 5$. So $f$ is

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