Differentiating Quadratics (and other polynomials)
- Author:
- jgregg
The definition of a derivative of a function
In the previous activity, you may have noticed the following formula.
gradient function
The first part of this is read as the limit as h tends to 0, it means we are interested in what happens as h approaches zero.
The next part asks us to evaluate a function at different points and divide by h. If we perform this calculation for the function let us see what happens
So
If we divide this expression by h we get
But remember I am interested in what happens as , so this evaluates to
This is the gradient function for
We can perform the same calculations for
Dividing by h gives
and since
the gradient function is
As an exercise, you could try to perform the same process for different quadratic, cubics and other polynomials. You may even like to try some other functions.