Second Derivative Test

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Example

Solve:

• f'(c) = 0 means c is a critical point, could be max, min, inflection.

• f''(c) < 0 means around point c it's a Downward Concave.

• Conclusion then is that c is a maximum point.

Example

Solve:

• f'(c) = 0 means c is a critical point, could be max, min, inflection.

• f''(c) = 0 means it's either a Concave up or down, we don't know yet.

• So the answer is "No enough information to tell."

Example

Solve:

• It's Concave Down when f''(x) < 0

• Find formula of f''(x) and set inequality equation f''(x)<0 and solve to get x > 2.