Download Understanding Tangent Lines A nonlinear relationship is a

Understanding Tangent Lines
A nonlinear relationship is a relationship between two variables that changes over the
range of the variables' values.
The slope of a nonlinear function changes at every point on it, reflecting the changing
relationship between the variables.
A tangent line is a straight line that touches a nonlinear curve at any point.
If a relationship between two variables is not
linear, the slope changes at different points on
the curve. These variables are said to have a
nonlinear relationship. To calculate the
slope exactly at a single point, you will have to
use calculus to take the limit.
If you use the "rise over run" calculation
between two points, as with a linear
relationship, the slope will change at every
point. For example, on the left, between
output levels of four TVs and sixteen TVs, the
slope is six.
Note that if you choose different points nearer
the bottom of this total product curve, the
slope becomes flatter.
Between output levels of four TVs and nine
TVs, the slope is five.
You must use calculus to find the slope of a
curvilinear line at any point. At the point you
are interested in, the slope of the curve equals
the slope of a tangent line at that point.
On the left, if you use calculus and find the
slope of the tangent line at the output level of
four TVs, the slope is four.
The important point is that the slope of a
nonlinear function changes over the curve.