### Reimann Sum:

The Reimann Sum of a function

*f* (

*x* ) over an interval [

*a*,

*b*] is defined as

where

*x*_{i-1} <

*x*_{i}^{*} <

*x*_{i}, and

*x*_{i}, and for

*i* = 1,…,

*n* divides the interval [

*a*,

*b*] into

*n* subintervals.

### Left Hand Sum:

The Left-Hand Sum of a function *f* ( *x* ) over an interval [*a*,*b*] is defined as where *x*_{i} for *i* = 1,…,*n *divides the interval [*a*,*b*] into *n* subintervals.### Right Hand Sum:

The Right-Hand Sum of a function *f* ( *x* ) over an interval [*a*,*b*] is defined as where *x*_{i} for *i* = 1,…,*n *divides the interval [*a*,*b*] into *n* subintervals.### Midpoint Sum:

The Midpoint Sum of a function *f* ( *x* ) over an interval [*a*,*b*] is defined as where , and *x*_{i} for *i* = 1,…,*n* divides the interval [*a*,*b*] into *n* subintervals.### Trapezoid Sum:

Trapezoid sum is the average between the Left Hand and Right Hand Sum.

### Average Value Of A Function:

The average value of a continuous function

*f* on the closed interval [

*a*,

*b*] is defined as

.

### Concavity:

This describes whether the function is curving up, down or not curving at all.

### Critical Point:

The derivative of the function at the critical point is 0.

### Inflection Point:

The point (

*x*-value) where the function changes concavity.

### Secant Line:

The line joining two points on the graph of a function.

### Tangent Line:

A line that touches the graph of a function

*f* (

*x*) at a point.

### Differentiability:

If the limit exists, the function

*f* (

*x*) is differentiable at

*x* =

*a*.