Now, let's think about how this relates to real graphs. Imagine you have a graph where the x-axis represents time (how long you've been biking) and the y-axis represents your speed. If we plot your speed at different times, the curve we get shows how your speed changes. The derivative of this curve at any given point tells us your instantaneous speed at that exact moment. In other words, if you look at the slope of the tangent line to the curve at any point, that's your speed right then. Just like on your bike ride, the steeper the hill (the steeper the tangent line), the faster you're going. So, the derivative helps us understand how quickly things are changing in real time.