Monkey Rule 0
The "first" Monkey Rule is really the 0th Monkey Rule. You probably aren't going to be surprised by it at all.
To lead you towards it, I ask you: What is the slope of all of the tangent lines of the linear function
f(x)=mx+b below?
Feel free to adjust m and b, and also to move A along f(x) to make conjectures and explore. As in earlier activities, point B was generated with the code (x(A),slope(g)) and is tracing the derivative of f(x).As we see above, the slope of the tangent line of a linear function is always just the slope of the linear function. The reason for this is simple: because linear functions are lines to begin with, their tangent lines are just themselves.
Since the slope of the tangent line to a linear function is just the slope of the linear function, we can deduce the 0th Monkey Rule
Monkey Rule 0: The derivative of a linear function
f(x)=mx+b is constant, and equal to the slope of the linear function. In other words f'(x)=m.
We can see Monkey Rule 0 in action above by noticing that as we move point A, we see that point B (which traces the derivative of f(x)) is always at height m above the x axis.
In the next activities we'll get into some more intricate Monkey Rules. Some people actually find them easier than this one since there's a bit more to latch onto. Onward!