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

**
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.

**
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.

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

**
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}
.

**
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}
.

**
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.

**
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.)

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

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