# Differential calculus: derivatives graphing tool

Learning Material  |  Interactive Lesson

Published on 2018 August 13th

Description
Use this revision tool to examine the relationship between functions and their derivatives by observing their graphs. Select a polynomial function (for example, f(x) = x³ – 3x²) from the menu. Estimate the gradients of the given tangents and position them on the graph of the function. Draw the graph of the derivative function. Use the slider to compare the values of the polynomial function and the derivative function. Complete the tasks for each polynomial function in the menu to continue exploring the visual relationship between the two graphs. This learning object is one in a series of ten objects.
Objective
Students interpret the gradient of the tangent to a curve as being the rate of change of the function.
Students apply the first principles method to differentiate basic polynomial functions.

#### 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