**
Differentiable
** -
A function
*f*
is said to be differentiable at a point
*x* = *a*
if
*f'*(*a*)
exists.

**
Difference Quotient
** -
The difference quotient,

represents the slope of an arbitrary secant line connecting the point

(*x*, *f* (*x*))
and the
nearby point

(*x* + *h*, *f* (*x* + *h*))
on the graph of

*f*
.

**
Derivative
** -
The derivative of

*f*
is denoted as

*f'*(*x*)
, and it is the function that gives the slope of
the graph of

*f*
at the point

(*x*, *f* (*x*))
. Written as the limit of the difference
quotient, the derivative of

*f* (*x*)
is

**
Secant
** -
The secant line is a line connecting two points on the same curve

**
Tangent
** -
The tangent to a curve is the line that just touches the curve at one point.
At the point where the tangent meets the curve, they have the same slope.