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Second Derivative Test Examples

Example 1

Let f (x) = xex. If possible, use the second derivative test to determine if each critical point is a maximum, a minimum, or neither.

Example 2

Let f (x) = -x3 + 3x2 – 3x. If possible, use the second derivative test to determine if each critical point is a minimum, maximum, or neither.

Example 3

Let f (x) = 5 – x2. If possible, use the second derivative test to determine if each critical point is a minimum, maximum, or neither.

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