#### First Derivative Test

#### Second Derivative Test

A point where the second derivative of a function changes sign, the graph of the function will switch from concave down to concave up, or vice versa, is called an inflection point. Assuming the second derivative is continuous, it must take a value of zero at any inflection point, although not every point where the second derivative is zero is necessarily a point of inflection.

#### Third Derivative Test

In mathematics, jerk is defined as the third derivative of the position function of an object. It is, essentially, the rate at which acceleration changes.

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