# Differential calculus: cubic function

Learning Material  |  Interactive Lesson

Published on 2018 August 13th

Description
Observe the non-linear distance–time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formula s(t) = t^3 – 2. Calculate the average velocity of the rocket over time intervals that become progressively shorter. Tabulate the results and look for a pattern. Use your knowledge of limits to derive a formula for finding the instantaneous velocity at a given point. 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 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 function s(t) = t^3 – 2.
Students interpret the concept of a derivative of a function, and identify that for s(t) = t^3 – 2 the derivative is f'(t) = 3t^2.

#### 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