Finding the Equation of a Tangent Line
Using the First Derivative
Certain problems in Calculus I call for using the first derivative to find the equation of the
tangent line to a curve at a specific point.
The following diagram illustrates these problems.
There are certain things you must remember from College Algebra (or similar classes)
when solving for the equation of a tangent line.
Recall :
• A Tangent Line is a line which locally touches a curve at one and only one point.
• The slope-intercept formula for a line is y = mx + b, where m is the slope of the
line and b is the y-intercept.
• The point-slope formula for a line is y – y1 = m (x – x1). This formula uses a
point on the line, denoted by (x1, y1), and the slope of the line, denoted by m, to
calculate the slope-intercept formula for the line.
Also, there is some information from Calculus you must use:
Recall:
• The first derivative is an equation for the slope of a tangent
line to a curve at an indicated point.
• The first derivative may be found using:
()()
h
xf−+
→
hxf
lim
:derivative a of definition The A)
0h
B) Methods already known to you for derivation, such as:
• Power Rule
• Product Rule
• Quotient Rule
• Chain Rule
(For a complete list and description of these rules see your text)
