Differential calculus: power functions

Learning Material  |  Interactive Lesson

Published on 2018 August 13th

Observe the non-linear graphs of various power functions (such as f(x) = x², or f(x) = x³) and select the expressions for finding the gradient of the secant between small changes in x represented by ?x. Tabulate the values of f'(x) and plot the derivative of each function. Determine the pattern between the graphs for each function. 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 functions of various powers of x.
Students interpret the concept of a derivative of a function, and identify the derivatives for various power functions of x.
Students investigate the derivative to calculate the range of a function at a nominated point.

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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