Welcome to Clip from Spiral logo

Interactive video lesson plan for: ❤︎² How to Find the Equation of a Tangent Line with Derivatives (mathbff)

Activity overview:

MIT grad shows how to find the equation of a tangent line using derivatives (Calculus). More videos with Nancy coming in 2017! To skip ahead: 1) For a BASIC example, skip to time 0:44. 2) For a more complex example that uses the CHAIN RULE, skip to time 5:58. 3) For an example that uses TRIG FUNCTIONS, skip to time 11:35.

What is a tangent line? It is a line that is tangent to a curve at one point. You can use calculus to find the tangent line by taking the derivative of the given equation. Here are the steps to finding the equation of the tangent line, using derivatives:

1) TAKE DERIVATIVE: The first step is to take the derivative of the given equation, with respect to x. For instance, to find the equation of the line tangent to f(x) = x^2 + 3 at x = 4, first take the derivative of f(x), which is 2x.

2) PLUG IN X-VALUE INTO DERIVATIVE TO GET SLOPE: The second step is to plug the given x-value into the derivative of f(x). The value you get is the slope of the tangent line, m.

3) FIND Y-VALUE OF POINT WITH ORIGINAL EQUATION: The third step is to find the y-value of the point. You get this by plugging the given x-value into the original equation to find the corresponding y-value. Since you want the tangent line at x = 4, plug x = 4 into the original f(x), and you get a y-value of 7. This means that the full point is (4,7).

4) PLUG THE SLOPE AND X,Y POINT VALUES INTO POINT-SLOPE EQUATION: The last step is to put the x and y point values, as well as the slope, m, into the point-slope equation of a line. The point-slope equation is x - x1 = m (y - y1). Plug the x and y point values into this equation for x1 and y1. Plug the slope you found in for m. This is the equation of the tangent line. The equation will still have x and y variables in it.

You can also rearrange the equation you get so that it is in "y equals" or slope-intercept form, if you want.

Tagged under: tangent line,tangent,line,derivative,curve,calculus,equation,slope,chain rule,power rule, derivative,point,coordinates,function,point slope equation,slope intercept form,point slope,slope intercept,linear,trig,trigonometry,numerator,denominator,simplify,-,rules,explanation,find,solve,solution, , cases,jmt,shortcut,trick,khan,math,mathematics,easy,test,tutor,problem,tips

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share ❤︎² How to Find the Equation of a Tangent Line with Derivatives (mathbff) on Google+ Share ❤︎² How to Find the Equation of a Tangent Line with Derivatives (mathbff) on Twitter Share ❤︎² How to Find the Equation of a Tangent Line with Derivatives (mathbff) on Facebook Pin ❤︎² How to Find the Equation of a Tangent Line with Derivatives (mathbff) Email ❤︎² How to Find the Equation of a Tangent Line with Derivatives (mathbff)

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Spiral
Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Spiral
Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Spiral
Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Spiral
Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Spiral
Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Spiral
Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome