# Differential calculus: non-linear graphs

Learning Material  |  Interactive Lesson

Published on 2018 August 13th

Description
Observe the non-linear distanceâ€“time graph of a rocket travelling at a changing velocity. Calculate the average and instantaneous velocity of the rocket over different time intervals. Notice how as each time interval becomes smaller, the rocket's average velocity approaches its instantaneous velocity. Use the slider to change the points where the secant intersects the curve and observe the gradient calculator. Work out the relationship between average and instantaneous velocities and the gradients of secants and tangents. This learning object is one in a series of ten objects. Some objects in the series are also packaged as combined learning objects.
Objective
Students identify that a non-linear function produces a curved graph.
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 the first principles method to differentiate basic polynomial functions.

#### Curriculum Information

 Education Type K to 12 Grade Level Grade 8, Grade 9, Grade 10 Learning Area Mathematics Content/Topic Patterns and Algebra Patterns and algebra Intended Users Learners, Students Competencies