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Aim: to investigate the gradient function for all kinds of curves. Research: What does "gradient" mean? Generally, the "steepness" of a curve is measured by its gradient. We can look at the figure below: This is the curve of y=x2. The point P (3, 9) has been marked and the tangent QPM drawn. The gradient of the tangent is QN/MN. So we can use the "tangent method" to obtain the gradients of graphs of different functions. First Step: I am going to investigate the gradient of y=x, y=x2, y=x3 first because they are likely to be the simplest equations to solve, and after getting these results easily, by looking at them, the more complex equations will seem easier to discover. I am going to look at y=x first because it is the easiest. x 1 2 3 4 y 1 2 3 4 Please see graph on separate pieces of paper As we see, the gradients of y=x is very simple, a=1. We even do not need...

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