Observe the non-linear distance-time graph of a rocket travelling at a changing velocity. Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and derive a formula for finding the instantaneous velocity at a given point. In the second activity, observe the non-linear graphs of various powers of x and select the expressions for finding the gradient of the secant between small intervals of x (represented by ?x). Plot the derivatives of each function and look for patterns. This learning object is a combination of two objects in the same series.
Objective
Students apply the concept of a limit in the context of the rate of change of a non-linear function.
Students interpret the gradient of the tangent to a curve as being the rate of change of the function.
Students apply first principles methods to differentiate the functions of t² and various powers of x.
Students interpret the concept of a derivative of a function, and identify the derivative for t² and for various power functions of x.
Students investigate the derivative to calculate the range of a function at a nominated point.
Curriculum Information
Education Type
K to 12
Grade Level
Grade 9, Grade 10
Learning Area
Mathematics
Content/Topic
Patterns and Algebra
Patterns and algebra
Intended Users
Learners, Students
Competencies
Copyright Information
Copyright
Yes
Copyright Owner
Education Sevices Australia
Conditions of Use
Use
Technical Information
File Size
0 bytes
File Type
application/x-rar
Software/Plug-in Requirements
Adobe Flash Player - http://get.adobe.com/flashplayer/
