The Dots Connected
That's right,
f'(x)=2x+2 because the y intercept is 2 and the slope is 2. It's plotted as the dashed line through the three red points from the previous activity.
Congratulations! You calculated your first derivative! Your first derivative is a new function called f'(x), and it keeps track of the slopes of these lines that very closely match f(x). We'll get more specific and explore this idea in several different ways shortly, so don't worry if you don't fully grasp the idea just yet.
Move the point A along f(x) again, and notice how the breadcrumbs seem to perfectly match f'(x).