Differential calculus: quartic function

Learning Material  |  Interactive Lesson

Published on 2018 August 13th

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^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 one in a series of ten objects. Some objects in the series are also packaged as combined learning objects.
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^4 + t^2.
Students interpret the concept of a derivative of a function, and identify that for s(t) = t^4 + t^2 the derivative is f'(t) = 4t^3 + 2t.

Curriculum Information

K to 12
Grade 9, Grade 10
Patterns and Algebra Patterns and algebra
Learners, Students

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Education Sevices Australia

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