Introduction to Derivatives

• Mathematics

Have you heard of the term "derivative" before? What do you think it means?

Which blue line demonstrates a line tangent to the curve?

1. 
2. 
3. 
4. 

Derivative Formula #1

Derivative Formula #2

Let's Practice with These Equations!

We'll start with Example 1 in your notes.  Here's the process when finding the derivative AT A POINT:

1.  Write the equation you will use.
2.  Fill in known information for f(a).  In this problem, we know that f(3)=6.
3. Substitute x into f(a) to complete your limit.
4. Simplify this expression using your knowledge of factoring.
5. Once you get a limit that can be solved (the denominator is not zero, substitute 3 into your expression and solve.

Test Yourself!

Try to perform Example 1 in your notes.  You can compare your work with mine on the next slide!

What if we needed the equation of the tangent line (Example 2)?

Well, we have a slope and a point.  Use point-slope form to generate an equation for the tangent line!

y - y1 = m(x - x1)

Is this making sense? Please let me know where you are confused!

Drag the function graphs above down to their matching derivative graphs below!

Let's try another one! 

Do example 7 in your notes, and then compare your work with mine on the next slide.  Try and use our formal limit equation!

Do you have any questions or areas of concern?

You are a SMART COOKIE, and you can do this!  Practice makes perfect.