AS/A2 Pure 1 Pure 2

P3 Topic 2: Coordinate geometry in the (x, y) plane
A decreasing function
The graph of the following rational function, where a, b and c are positive constants, is shown in black, together with its gradient function dy/dx in red.
How do these graphs show you that y is always decreasing?

Summary y is always decreasing because: the gradient of its graph is always negative the curve of the gradient function is always below the x axis dy/dx < 0 for all values of x Based on free Java applets from JavaMath