Derivative Definition Lesson
Definition of a Derivative
- Click on "First Point". This is the point at which you want to find the derivative.
- Click on "Second Point". This is a variable point that will help you find the derivative
- Click on "Secant Line". This is the line through and . Write the slope formula for the secant line on a piece of paper (because you will need it later)
- Move "h" so that it "approaches 0". Write the limit expression involving what you wrote in part 3 and "h approaching 0"
- Move "a" around and take note of the behavior of the slope of the tangent line. Where is it positive? Where is it negative? Where is it 0?
- Now change the function to and repeat #5.
- Change the function to and repear #5.
Slope of Secant and Tangent Line
The parabola
Using the graph of , which of the following statements are true about
The parabola
Using the graph of , which of the following statements are true about
The parabola
Using the graph of , which of the following statements are true about
The cubic
Using the graph of , which of the following statements are true about
The cubic
Using the graph of , which of the following statements are true about
The cubic
Using the graph of , which of the following statements are true about
The sine graph
Using the graph of , which of the following statements are true about
The Exponential Graph
Using the graph of , which of the following statements are true about
The Log Graph
Using the graph of , which of the following statements are true about
The Absolute Value Graph
Using the graph of , which of the following statements are true about
Fill in the blank
When the graph of is increasing, then is
Fill in the blank
When the graph of is decreasing, then is
Fill in the blank
When the graph of has a corner, then is