More About The Tan Gents

Beach Buddies by rcktmanil

http://www.math.hmc.edu/calculus/tutorials/tangent_line/

All about tangent lines.

Some Pre-Calculus Material You Should Recall 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 . This formula uses a point on the line, denoted by , and the slope of the line, denoted by m, to calculate the slope-intercept formula for the line.

• Parallel lines have equivalent slopes.

• Perpendicular lines have slopes whose product is -1. i.e.

Some Calculus You Should Recall:

• The first derivative is an equation tells you the slope of a tangent line at any point.

• The first derivative may be found using:

(a)

(b) Methods already known to you for derivation, such as:

• Power Rule • Product Rule • Quotient Rule • Chain Rule

A New Definition Using Old Ideas

A Normal Line: A normal line is a line that is perpendicular to a tangent line at a point.

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http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/tangents.html

Find the equation of the tangent line at the given point for each function.

at x = -1 at x = 3

Find the equation of the normal line at the given point for each function.

at x = -3at x = 1

For each function, find all points where the tangent line is horizontal.