# Differential calculus: cubic and quartic functions

Learning Material  |  Interactive Lesson

Published on 2018 August 13th

Description
Observe the non-linear time graph of a rocket travelling at a changing velocity. The distance, s, travelled by the rocket after t seconds is determined by the formulas: s(t) = t^3 – 2 and s(t) = t^4 + t^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 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: s(t) = t^3 – 2 and s(t) = t^4 + t^2.
Students interpret the concept of a derivative of a function. They identify that for s(t) = t^3 – 2 the derivative is f'(t) = 3t^2, and that for s(t) = t^4 + t^2 the derivative is f'(t) = 4t^3 + 2t.

#### 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