How can I determine the characteristics of a curve on an x-y set of axis (eg. points of intersection, stationary points, area under graph)?

To determine the characteristics of a graph, we need to examine what we are been shown in the question. Below is an exam style question:By looking at both the graph and the equation, we can see that in the predefined region the curve has two points of intersection. We can determine both of these points by using the nature that, on the x-axis y=0 and on the y-axis x=0. Using these two identities, we can find from the equation of the curve that point B is (3,0) and O is (0,0). To determine the point A, we will need to differentiate the equation of the curve. This gives us:dydx=1.5x-0.5-1.5x0.5At the stationary point, dy/dx=0. Solving this equation gives us A as approximately (1,2). Finally to find the area under the curve we will need to integrate the equation between the limits of O and B. This gives:033x0.5-x1.5dx = 4527