12.3: Tangent Lines and introduction to derivatives

A tangent line is a line at point P that has the best approximating of the graph at that point. Here are some examples of graphs with points of tangency.

For this lesson it will also be important to remember slope. 

Slope is defined as change in x/change in y. 

The equation used to find the slope of line tangent to a graph at any given point is: 

To solve, you will need to substitute the given equations into the formula. 

Here are some examples of some problems: 

Another word for the slope of the line that is tangent to the graph is derivative. The derivative is denoted as f'(x) and read as f prime x. 

Here are some examples of finding the derivative: 

One shortcut to finding the derivative is the polynomial derivatives shortcut, but it will only work for equations in polynomial form. This can be summed up as "bring down the power and decrease by 1."

Here are some examples of finding the derivative by the polynomial shortcut: 

Math joke of the day: