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Critical Point
** -
A number *x* in the domain of a function *f* such that *f'*(*x*) = 0.

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Global Maximum
** -
A value *f* (*x*_{0}) that is greater than or equal to any other value *f* (*x*) that *f* takes on
over its domain.

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Global Minimum
** -
A value *f* (*x*_{0}) that is less than or equal to any other value *f* (*x*) that *f* takes on over
its domain.

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Inflection Point
** -
A number *x* in the domain of a function *f* such that *f*’’(*x*) = 0.

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Local Maximum
** -
A value *f* (*x*_{0}) that is greater than or equal to any other value *f* (*x*) for *x* in some
interval about *x*_{0}.

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Local Minimum
** -
A value *f* (*x*_{0}) that is less than or equal to any other value *f* (*x*) for *x* in some
interval about *x*_{0}.

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First Derivative Test
** -
A critical point *x*_{0} of a function *f* is a local maximum if the first derivative *f'* changes sign from
positive to negative at *x*_{0}. Correspondingly, *x*_{0} is a local minimum is *f'* changes sign from
negative to positive there.

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Second Derivative Test
** -
A critical point *x*_{0} of a function *f* is a local maximum if the second derivative *f''*(*x*_{0}) is
negative. It is a local minimum if *f''*(*x*_{0}) is positive. (It is also possible that *f''*(*x*_{0}) = 0, in
which case the critical point is also an inflection point.)

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Concave Up
** -
A function *f* (*x*) is *concave up* at *x*_{0} if *f''*(*x*_{0}) > 0.

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Concave Down
** -
A function *f* (*x*) is *concave down* at *x*_{0} if *f''*(*x*_{0}) < 0.