L3 Finding Tangent Lines Along Curves - Part 1
Completion requirements
Unit 2B
Derivatives Part 2
Lesson 3: Finding Tangent Lines Along Curves
When derivatives were first introduced, they were repeatedly connected to the slope of a tangent line. Knowing that a function’s derivative gives the slope of the function, how can the equation of the tangent line be determined? What about the equation
of a normal line, which is a line perpendicular to a tangent line, as shown in the diagram?
In Unit 2A Lesson 1, the process of how a secant line becomes a tangent line to a curve was discussed. In Unit 2A Lesson 2, the relationships between the derivative of a function and the slope of the line tangent to its curve was discussed. This Lesson will focus on writing the equations of lines tangent and normal to curves.
Recall there are three different ways to write the equation of a line.
In Unit 2A Lesson 1, the process of how a secant line becomes a tangent line to a curve was discussed. In Unit 2A Lesson 2, the relationships between the derivative of a function and the slope of the line tangent to its curve was discussed. This Lesson will focus on writing the equations of lines tangent and normal to curves.
Recall there are three different ways to write the equation of a line.
- slope – intercept form, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»y«/mi»«mo»=«/mo»«mi»m«/mi»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«/mrow»«/mstyle»«/math»
- slope – point form, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»y«/mi»«mo»§#8722;«/mo»«msub»«mi»y«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mi»m«/mi»«mi mathvariant=¨normal¨»(«/mi»«mi»x«/mi»«mo»§#8722;«/mo»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mi
mathvariant=¨normal¨»)«/mi»«/mrow»«/mstyle»«/math»
- general form of a line, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi»A«/mi»«mi»x«/mi»«mo»+«/mo»«mi»B«/mi»«mi»y«/mi»«mo»+«/mo»«mi»C«/mi»«mo»=«/mo»«mn»0«/mn»«/mrow»«/mstyle»«/math»
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