# Differential calculus: linear and non-linear graphs

Learning Material  |  Interactive Lesson

Published on 2018 August 13th

Description
Observe the linear and non-linear distanceâ€“time graphs of a rocket travelling at both constant and changing velocities. Calculate the average and instantaneous velocities of the rocket over different time intervals. Notice what happens to the average and instantaneous velocities as the time intervals become smaller. Work out the relationship between these velocities and the gradients of secants and tangents. This learning object is a combination of two objects in the same series.
Objective
Students interpret the gradient of a graph, and the gradient of the tangent to a curve, as being the rate of change of the function.
Students identify that a linear function produces a straight line graph.
Students identify that a non-linear function produces a curved graph.
Students predict that the average and instantaneous velocity of a linear function will always be the same at any given point on the graph.
Students apply the concept of a limit in the context of the rate of change of a 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