First, consider the function:
Spend some moments investigating
how to move the arrows, "Mark points" and "Clear marked points"
on the light blue grid at the left. 
Then consider the green grid on
the right.
The red curve is the graph of the
functionand the blue curve is the graph of
its
derivative.

On the left blue grid,
the
original parameters were a
= 0 and b = 0.
Moving the points about the surface changes the values of aand b.

By only
changing "a" in this graph,the
derivative retains a value of ( 0, 0 ).
This is another way of
saying that changes in "a" do not move the derivative from the origin.

[Note: In translation of functions, the
vertical motion correlates to the sign of the constant term.]


