Students can used their graphing calculators to build an understanding for the formal definition of a derivative (limit as h approaches zero of (f(x+h)-f(x))/h). Students will set up the forward difference quotient, the backward difference quotient, and the symmetric difference quotient approaching the same limit. Then students will let h equal 1, 0.1, 0.01, and 0.001) to notice that all the difference quotients approach one function.
The function they are all approaching will be called the derivative of the original function.
This is a great activity to use with the students prior to working analytically with the students to find the derivative of many basic functions. It gives the students a visual picture of what is happening to the difference quotients as h approaches zero.
Students can use this activity to develop all the basic derivative rules that they will need to memorize in Calculus.
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