The diagram below summarizes what we’ve just learned. A(x) derivative→ y(x) derivative→ dy/dx area under curve curve slope of curve It shows the three functions we’re interested in and the relationships between them. The given curve is in the middle, its unknown slope is on the right, and its unknown area is on the left. As we saw in chapter 6, these are the functions that occur in the three central problems of calculus. Given the curve y, we are trying to figure out its slope and its area.
