Why not look at a bunch of slopes at once?

Create the curve y=x^2 and look at the slope of the tangent line:

Using Animation, we can create a graph of the slope against the x-coordinate of A.  Where does the slope change from negative to positive?

The slope function is itself a straight line.  What is its equation?  We can draw a straight line over the top of it and select it to look at the slope’s equation.

What if we started off with y = 0.5*x^2?  Or x^2-3*x?  What would our slope equation look like?

SHHH - don’t mention the word calculus